Reverse engineering quantum field theory
NASA Astrophysics Data System (ADS)
Oeckl, Robert
2012-12-01
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
NASA Astrophysics Data System (ADS)
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Candidate General Ontologies for Situating Quantum Field Theory
NASA Astrophysics Data System (ADS)
Simons, Peter
Ontology is traditionally an a priori discipline purveying its categories and principles independently of mere facts, but this arrogance of philosophers has led them into latent or patent incompatibility with good science and has landed them with philosophical aporiai such as the mind-body problem and the universals dispute. So while maintaining the abstractness and systematic universality of ontology it pays to craft one's categories with an eye to the best empirical science, while not necessarily trying to read the ontology off that science. I present desiderata for a systematic ontology and give several reasons why one cannot use physical theory alone as the source of one's a posteriori ontology. With this in mind I survey six ontological theories as possible frameworks for QFT, four briefly, two at greater length. The first is the traditional substanceattribute metaphysic, which is clearly obsolete, and on which I expend little time. The second is its modern logico-linguistic replacement, the ontology of individuals and sets touted as semantic values in logical semantics. This too falls by the wayside for several reasons. A third is the closely related ontology or ontologies of facts, against which I argue on general grounds. A fourth is Whiteheadian process ontology, which is an improvement over the previous three but still leaves several questions unsatisfactorily answered. The most flexible and promising to date is the ontology of tropes and trope bundles, which I have discussed in several places. After expounding this I reject it not because it is false but because it is neither broad nor deep enough. As a final, sixth alternative, I present an ontology of invariant factors inspired in part by Whitehead and in part by remarks of Max Planck, and offer it as a promising future abstract framework within which to situate the physics of QFT.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
General quantum-mechanical setting for field-antifield formalism as a hyper-gauge theory
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-09-01
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schr\\"odinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schr\\"odinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.
Computational quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, Rainer
2006-05-01
I will give an overview on recent attempts to solve the time-dependent Dirac equation for the electron-positron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electron-positron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pair-production due to the supercriticality of the potential together with the scattering at the barrier involving the Pauli-principle. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
NASA Astrophysics Data System (ADS)
Weinberg, Steven
1996-08-01
In this second volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly expoistion of quantum theory. Volume 2 provides an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Exercises are included at the end of each chapter.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory.
Burgess, Cliff P
2004-01-01
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.
Quantum Field Theory, Revised Edition
NASA Astrophysics Data System (ADS)
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Quantum cellular automata and free quantum field theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Changing Views of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2010-03-01
The first part of this talk reviews changes in our views regarding quantum field theory since its beginnings, leading eventually to the modern view that our most successful field theories may in fact be effective field theories, valid only as low energy approximations to an underlying theory that may not be a field theory at all. In the second part, I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory, and finally cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe. The second part is substantially the same as a talk given a month earlier at the 6th International Workshop on Chiral Dynamics, at the University of Bern, which is reproduced here.
Renormalization group equations and matching in a general quantum field theory with kinetic mixing
NASA Astrophysics Data System (ADS)
Fonseca, Renato M.; Malinský, Michal; Staub, Florian
2013-11-01
We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Quantum field theory of treasury bonds.
Baaquie, B E
2001-07-01
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
NASA Astrophysics Data System (ADS)
Colosi, Daniele; Dohse, Max
2017-04-01
We use the General Boundary Formulation (GBF) of Quantum Field Theory to compute the S-matrix for a general interacting scalar field in a wide class of curved spacetimes. As a by-product we obtain the general expression of the Feynman propagator for the scalar field, defined in the following three types of spacetime regions. First, there are the familiar interval regions (e.g. a time interval times all of space). Second, we consider the rod hypercylinder regions (all of time times a solid ball in space). Third, the tube hypercylinders (all of time times a solid shell in space) are related to interval regions, and result from removing a smaller rod from a concentric larger one. Using the Schrödinger representation for the quantum states combined with Feynman's path integral quantization, we obtain the S-matrix as the asymptotic limit of the GBF amplitude associated with finite interval, and rod regions. For interval regions, whose boundary consists of two Cauchy surfaces, the asymptotic GBF-amplitude becomes the standard S-matrix. Our work generalizes previous results (obtained in Minkowski, Rindler, de Sitter, and Anti de Sitter spacetimes) to a wide class of curved spacetimes.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum simulation of quantum field theories in trapped ions.
Casanova, J; Lamata, L; Egusquiza, I L; Gerritsma, R; Roos, C F; García-Ripoll, J J; Solano, E
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum equivalence of dual field theories
NASA Astrophysics Data System (ADS)
Fradkin, E. S.; Tseytlin, A. A.
1985-06-01
Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrödinger theory.
Pilot-wave theory and quantum fields
NASA Astrophysics Data System (ADS)
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Dynamical Correspondence in a Generalized Quantum Theory
NASA Astrophysics Data System (ADS)
Niestegge, Gerd
2015-05-01
In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras). One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders-von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin (Mod Phys Lett A 9:3119-3127, 1994) and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them.
Quantum Algorithms for Fermionic Quantum Field Theories
2014-04-28
a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by...in fermionic field theories, exemplified by the massive Gross- Neveu model, a theory in two spacetime dimensions with quartic interactions. The...two spacetime dimensions with quartic interactions. Although our analysis is specific to this theory, our algorithm can be adapted to other massive
Exact integrability in quantum field theory
Thacker, H.B.
1980-08-01
The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)
Arrival time in quantum field theory
NASA Astrophysics Data System (ADS)
Wang, Zhi-Yong; Xiong, Cai-Dong; He, Bing
2008-09-01
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.
Charge transfer in algebraic quantum field theory
NASA Astrophysics Data System (ADS)
Wright, Jill Dianne
We discuss aspects of the algebraic structure of quantum field theory. We take the view that the superselection structure of a theory should be determinable from the vacuum representation of the observable algebra, and physical properties of the charge. Hence one determines the nature of the charge transfer operations: the automorphisms of the observable algebra corresponding to the movement of charge along space-time paths. New superselection sectors are obtained from the vacuum sector by an automorphism which is a limit of charge transfer operations along paths with an endpoint tending to spacelike infinity. Roberts has shown that for a gauge theory of the first kind, the charge transfer operations for a given charge form a certain kind of 1-cocycle over Minkowski space. The local 1-cohomology group of their equivalence classes corresponds to the superselection structure. The exact definition of the cohomology group depends on the properties of the charge. Using displaced Fock representations of free fields, we develop model field theories which illustrate this structure. The cohomological classification of displaced Fock representations has been elucidated by Araki. For more general representations, explicit determination of the cohomology group is a hard problem. Using our models, we can illustrate ways in which fields with reasonable physical properties depart fromthe abovementioned structure. In 1+1 dimensions, we use the Streater-Wilde model to illustrate explicitly the representation-dependence of the cohomology structure, and the direction-dependence of the limiting charge transfer operation. The cohomology structure may also be representation-dependent in higher-dimensional theories without strict localization of charge, for example the electromagnetic field. The algebraic structure of the electromagnetic field has many other special features, which we discuss in relation to the concept of charge transfer. We also give some indication of the modifications
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Dirac's equation and the nature of quantum field theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2012-11-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Protected gates for topological quantum field theories
Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit
2016-02-15
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
On space of integrable quantum field theories
NASA Astrophysics Data System (ADS)
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Quantum field theory of the Casimir effect for real media
Mostepanenko, V.M.; Trunov, N.N.
1985-11-01
The quantum field theory is developed for the corrections to the Casimir force arising when the field penetrates the material of the plates. A new type of divergence arising from the corresponding modification of the boundary conditions is analyzed. General expressions are obtained for the vacuum energy of the electromagnetic field in the space between nonideal plates, and the actual corrections to the Casimir force are calculated in first-order perturbation theory in the penetration depth.
Effective Particles in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Głazek, Stanisław D.; Trawiński, Arkadiusz P.
2017-03-01
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead integrates out the large changes of invariant mass. The new procedure is explained using examples of known interactions. Some applications in phenomenology, including processes measurable in colliders, are briefly presented.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Quantum simulation of quantum field theory using continuous variables
NASA Astrophysics Data System (ADS)
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2015-12-01
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Infinite-time average of local fields in an integrable quantum field theory after a quantum quench.
Mussardo, G
2013-09-06
The infinite-time average of the expectation values of local fields of any interacting quantum theory after a global quench process are key quantities for matching theoretical and experimental results. For quantum integrable field theories, we show that they can be obtained by an ensemble average that employs a particular limit of the form factors of local fields and quantities extracted by the generalized Bethe ansatz.
Quantum Field Theory in Condensed Matter Physics
NASA Astrophysics Data System (ADS)
Tsvelik, Alexei M.
2007-01-01
Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34
Generalized IIB supergravity from exceptional field theory
NASA Astrophysics Data System (ADS)
Baguet, Arnaud; Magro, Marc; Samtleben, Henning
2017-03-01
The background underlying the η-deformed AdS 5 × S 5 sigma-model is known to satisfy a generalization of the IIB supergravity equations. Their solutions are related by T-duality to solutions of type IIA supergravity with non-isometric linear dilaton. We show how the generalized IIB supergravity equations can be naturally obtained from exceptional field theory. Within this manifestly duality covariant formulation of maximal supergravity, the generalized IIB supergravity equations emerge upon imposing on the fields a simple Scherk-Schwarz ansatz which respects the section constraint.
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
Generalized conservation laws in non-local field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories.
Sulejmanpasic, Tin
2017-01-06
We discuss quantum field theories with global SU(N) and O(N) symmetries for which temporal direction is compactified on a circle of size L with periodicity of fields up to a global symmetry transformation, i.e., twisted boundary conditions. Such boundary conditions correspond to an insertion of the global symmetry operator in the partition function. We argue in general and prove in particular for CP(N-1) and O(N) nonlinear sigma models that large-N volume independence holds. Further we show that the CP(N-1) theory is free from the Affleck phase transition confirming the Ünsal-Dunne continuity conjecture.
Symmetries in Three-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
Bashkirov, Denis
Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ≥ 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].
Cluster-like coordinates in supersymmetric quantum field theory
Neitzke, Andrew
2014-01-01
Recently it has become apparent that N=2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1–211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore. PMID:24982190
Cluster-like coordinates in supersymmetric quantum field theory.
Neitzke, Andrew
2014-07-08
Recently it has become apparent that N = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.
Gauge-fields and integrated quantum-classical theory
Stapp, H.P.
1986-01-01
Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs.
Pfalzgraff, William C; Kelly, Aaron; Markland, Thomas E
2015-12-03
The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.
Axiomatics of Galileo-invariant quantum field theory
Dadashev, L.A.
1986-03-01
The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
Multi-time wave functions for quantum field theory
Petrat, Sören; Tumulka, Roderich
2014-06-15
Multi-time wave functions such as ϕ(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.
Euclidean quantum field theory: Curved spacetimes and gauge fields
NASA Astrophysics Data System (ADS)
Ritter, William Gordon
This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on four-dimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories on curved spacetimes. The success of Euclidean path integrals to capture nonperturbative aspects of QFT has been striking. The Euclidean path integral is the most accurate method of calculating strong-coupling effects in gauge theory (such as glueball masses). Euclidean methods are also useful in the study of black holes, as evidenced by the Hartle-Hawking calculation of black-hole radiance. From a mathematical point of view, on flat spacetimes the Euclidean functional integral provides the most elegant method of constructing examples of interacting relativistic field theories. Yet until now, the incredibly-useful Euclidean path integral had never been given a definitive mathematical treatment on curved backgrounds. It is our aim to rectify this situation. Along the way, we discover that the Dirac operator on an arbitrary Clifford bundle has a resolvent kernel which is the Laplace transform of a positive measure. In studying spacetime symmetries, we discover a new way of constructing unitary representations of noncompact Lie groups. We also define and explore an interesting notion of convergence for Laplacians. The same mathematical framework applies to scalar fields, fermions, and gauge fields. The later chapters are devoted to gauge theory. We present a rigorous, self-contained introduction to the subject, aimed at mathematicians and using the language of modern mathematics, with a view towards nonperturbative renormalization in four dimensions. The latter ideas are unfinished. A completion of the final chapter would imply the construction
Torque anomaly in quantum field theory
NASA Astrophysics Data System (ADS)
Fulling, S. A.; Mera, F. D.; Trendafilova, C. S.
2013-02-01
The expectation values of energy density and pressure of a quantum field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch-Candelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.
Noncommutative Common Cause Principles in algebraic quantum field theory
Hofer-Szabo, Gabor; Vecsernyes, Peter
2013-04-15
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.
Quantum field theory results for neutrino oscillations and new physics
Delepine, D.; Gonzalez Macias, Vannia; Khalil, Shaaban; Lopez Castro, G.
2009-05-01
The CP asymmetry in neutrino oscillations, assuming new physics at production and/or detection processes, is analyzed. We compute this CP asymmetry using the standard quantum field theory within a general new physics scenario that may generate new sources of CP and flavor violation. Well-known results for the CP asymmetry are reproduced in the case of V-A operators, and additional contributions from new physics operators are derived. We apply this formalism to SUSY extensions of the standard model where the contributions from new operators could produce a CP asymmetry observable in the next generation of neutrino experiments.
Analysis of general power counting rules in effective field theory
NASA Astrophysics Data System (ADS)
Gavela, Belen; Jenkins, Elizabeth E.; Manohar, Aneesh V.; Merlo, Luca
2016-09-01
We derive the general counting rules for a quantum effective field theory (EFT) in {d} dimensions. The rules are valid for strongly and weakly coupled theories, and they predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of the cross sections is controlled by the Λ power counting of EFT, not by chiral counting, even for chiral perturbation theory (χ PT). The relation between Λ and f is generalized to {d} dimensions. We show that the naive dimensional analysis 4π counting is related to hbar counting. The EFT counting rules are applied to χ PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.
Avoiding Haag's Theorem with Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Ed
2017-03-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.
The principle of stationary variance in quantum field theory
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2014-02-01
The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.
Quantum field theory on toroidal topology: Algebraic structure and applications
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
2014-05-01
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RD-d is developed from a Lie-group representation and c*c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real- and imaginary-time versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on
Radiation reaction in quantum field theory
NASA Astrophysics Data System (ADS)
Higuchi, Atsushi
2002-11-01
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant α and in the small ħ approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit.
Motivating quantum field theory: the boosted particle in a box
NASA Astrophysics Data System (ADS)
Vutha, Amar C.
2013-07-01
It is a maxim often stated, yet rarely illustrated, that the combination of special relativity and quantum mechanics necessarily leads to quantum field theory. An elementary illustration is provided using the familiar particle in a box, boosted to relativistic speeds. It is shown that quantum fluctuations of momentum lead to energy fluctuations, which are inexplicable without a framework that endows the vacuum with dynamical degrees of freedom and allows particle creation/annihilation.
Nonperturbative studies in quantum field theory
Abada, A.
1992-01-01
This dissertation is composed of three different research topics. The first part deals with the Study of the so-called local lattice Yukawa theory. The motivation for this study is to investigate the interior of the phase diagram of this theory. A strong y expansion (y being the bare Yukawa coupling) is performed of the partition function and show that within the (finite) range of convergence of the series expansion, the lattice Yukawa theory is equivalent to a purely bosonic theory, with a shifted action. The author explicitly calculated the shifted action to the fourth order in 1/y and find that it is composed of competing interactions. This suggests that away from y = [infinity] towards the interior of the phase diagram, there is a more complicated ordering than simple ferromagnetic or antiferromagnetic. In the second part, the question is addressed of formation of bound states out of constituent fields in an exactly soluble theory, i.e. multifermion electro-dynamics in two space-time dimensions. The author exactly calculates the correlation function corresponding to a neutral composite fermion operator and discuss the pole structure of its Fourier transform. It does not exhibit a simple pole in p[sup 2], hence the corresponding neutral composite operator does not create an asymptotic state in the spectrum of the theory. In part three, the author puts multifermion QED[sub 2] in a heat bath and address the same question as in part two. The author first exactly calculates a bosonic correlation function at finite temperature and density, and discuss its behavior. The author then exactly calculates the correlation function corresponding to the neutral composite fermion operator at finite temperature and density and discusses its behavior. It is concluded that the temperature does not help the composite fermion operator create a particle in the spectrum of the theory.
Splitting fields and general differential Galois theory
Trushin, Dmitry V
2010-11-11
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
Quantum Field Theory of Kosterlitz-Thouless Phase Transitions.
NASA Astrophysics Data System (ADS)
Ogilvie, Michael Charles
1980-12-01
A general quantum field-theoretic formalism for the study of Kosterlitz-Thouless phase transition is developed and applied to several models. The structure of the free, massless scalar field is discussed, making explicit its connection with the Gaussian model. The close connection of the spin-wave and vortex operators with two-dimensional fermion-boson equivalences is stressed. The critical behavior of the planar model is reviewed, using field-theoretic methods applied to the sine-Gordon model. The Kosterlitz -Thouless phase transition in two-dimensional dislocation -mediated melting is studied using a vector generalization of the sine-Gordon model. Recent second-order renormalization group calculations are confirmed, and the issue of universal third-order corrections is discussed. It is shown that the Gross-Neveu model can be interpreted as a massive theory associated with a Kosterlitz-Thouless critical point. Finally, the Ising and Baxter models are studied using the methods developed here. It is shown that the vortex and spin-wave excitations in the Ising model conspire to produce a free, massive Majorana fermion field theory in the continuum limit. The formalism is then extended to the Baxter model. Recent results on the Baxter and Ashkin-Teller models are rederived and extended.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Giacosa, Francesco
2014-10-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
Constraints on RG flow for four dimensional quantum field theories
NASA Astrophysics Data System (ADS)
Jack, I.; Osborn, H.
2014-06-01
The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve a, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric G on the space of couplings and give rise to gradient flow like equations for a, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings e2σ to a form which involves running couplings gσ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa β-functions for a general scalar/fermion theory are obtained and the three loop contribution to the metric G for this theory is also calculated. These results are used to check the gradient flow equations to higher order than previously. It is shown that these are only valid when β→B, a modified β-function, and that the equations provide strong constraints on the detailed form of the three loop Yukawa β-function. N=1 supersymmetric Wess-Zumino theories are also considered as a special case. It is shown that the metric for the complex couplings in such theories may be restricted to a hermitian form.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Quantum field theory in non-integer dimensions
Eyink, G.L.
1987-01-01
In a 1973 paper entitled Quantum Field-Theory Models in Less Than 4 Dimensions, Kenneth G. Wilson studied field-theories for spacetime dimension d between 2 and 4. With unconventional renormalizations, these models were found to have non-Gaussian ultraviolet renormalization group fixed points. Wilson's method was perturbative dimensional regularization: the Feynman-graph integrals were analytically continued to non-integer d. His work left open the question of the nonperturbative existence of the models. Since that landmark paper, Yuval Gefen, Amnon Aharony and Benoit B. Mandelbrot have shown that Ising spin models on fractal lattices have critical properties like those predicted for non-integer dimensions by the analytic continuation, or {epsilon}-expansion method. This work shows that fractal lattices and continua provide also a nonperturbative definition of field-theories in non-integer dimensions. The fractal point-sets employed are the Sierpinski carpets and their higher-dimensional generalizations. This class of point-sets has a tunable dimension which allows the approach to four from below. Furthermore, the carpets have discrete groups of scale or dilation invariances and infinite order of ramification. A class of scalar field models are defined on these sets which should reduce to the standard models when d {nearrow}4. The propagator for these models is given by a proper-time or heat-kernel representation. For this propagator, reflection-positivity is established, a general scaling law is conjectured (and established in a special case), and the perturbative renormalizability shown to be governed by the spectral dimensionality. Scalar models with another choice of propagator, the hierarchical propagator, are studied by rigorous renormalization-group methods.
Quantum Field Theory and Decoherence in the Early Universe
NASA Astrophysics Data System (ADS)
Koksma, J. F.
2011-06-01
Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop stress-energy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantum-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired
Hydrodynamic transport functions from quantum kinetic field theory
NASA Astrophysics Data System (ADS)
Calzetta, E. A.; Hu, B. L.; Ramsey, S. A.
2000-06-01
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with λΦ4 self-interaction we need to include four-loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D 53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear-response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires a clever rendition of diagrammatic resummations which is neither straightforward nor fail-safe. Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-Abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quantum group symmetry of N=1 superconformal field theories
NASA Astrophysics Data System (ADS)
Jiménez, F.
1990-12-01
We use the Gómez-Sierra contour deformation techniques to show that N=1 superconformal field theories with {2c}/{3<1}, in their Coulomb gas version, contain a quantum group structure as an underlying symmetry. In particular, we construct from the thermal subalgebras of these theories, the representation spaces of the quantized universal enveloping superalgebra U q osp(2, 1) and show how to compute its R-matrix, the comultiplication rules and its quantum Clebsch-Gordan coefficients by using a convenient definition of the screened vertex operators and an explicit realization of its generators.
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf; Ludwig, Thomas; Verch, Rainer
2013-02-15
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
Quantum Entanglement of Local Operators in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-01
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
Combinatorial Hopf Algebras in Quantum Field Theory I
NASA Astrophysics Data System (ADS)
Figueroa, Héctor; Gracia-Bondía, José M.
This paper stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an elementary invitation to the subject as well. The rest of Sec. 1 is devoted to the basics of Hopf algebra theory and examples in ascending level of complexity. Section 2 turns around the all-important Faà di Bruno Hopf algebra. Section 2.1 contains a first, direct approach to it. Section 2.2 gives applications of the Faà di Bruno algebra to quantum field theory and Lagrange reversion. Section 2.3 rederives the related Connes-Moscovici algebras. In Sec. 3, we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Sec. 3.1, we describe the first. Then in Sec. 3.2, we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Sec. 3.3, general incidence algebras are introduced, and the Faà di Bruno bialgebras are described as incidence bialgebras. In Sec. 3.4, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained. The structure results for commutative Hopf algebras are found in Sec. 4. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.
Quantum field theory on curved spacetimes: Axiomatic framework and examples
NASA Astrophysics Data System (ADS)
Fredenhagen, Klaus; Rejzner, Kasia
2016-03-01
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
Dissipative quantum transport in macromolecules: Effective field theory approach
NASA Astrophysics Data System (ADS)
Schneider, E.; a Beccara, S.; Faccioli, P.
2013-08-01
We introduce an atomistic approach to the dissipative quantum dynamics of charged or neutral excitations propagating through macromolecular systems. Using the Feynman-Vernon path integral formalism, we analytically trace out from the density matrix the atomic coordinates and the heat bath degrees of freedom. This way we obtain an effective field theory which describes the real-time evolution of the quantum excitation and is fully consistent with the fluctuation-dissipation relation. The main advantage of the field-theoretic approach is that it allows us to avoid using the Keldysh contour formulation. This simplification makes it straightforward to derive Feynman diagrams to analytically compute the effects of the interaction of the propagating quantum excitation with the heat bath and with the molecular atomic vibrations. For illustration purposes, we apply this formalism to investigate the loss of quantum coherence of holes propagating through a poly(3-alkylthiophene) polymer.
Cold atom simulation of interacting relativistic quantum field theories.
Cirac, J Ignacio; Maraner, Paolo; Pachos, Jiannis K
2010-11-05
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
NASA Astrophysics Data System (ADS)
Peskin, Michael E.
2011-04-01
Anthony Zee is not only a leading theoretical physicist but also an author of popular books on both physics and non-physics topics. I recommend especially `Swallowing Clouds', on Chinese cooking and its folklore. Thus, it is not surprising that his textbook has a unique flavor. Derivations end, not with `QED' but with exclamation points. At the end of one argument, we read `Vive Cauchy!', in another `the theorem practically exudes generality'. This is quantum field theory taught at the knee of an eccentric uncle; one who loves the grandeur of his subject, has a keen eye for a slick argument, and is eager to share his repertoire of anecdotes about Feynman, Fermi, and all of his heroes. A one-page section entitled `Electric Charge' illustrates the depth and tone of the book. In the previous section, Zee has computed the Feynman diagram responsible for vacuum polarization, in which a photon converts briefly to a virtual electron-positron pair. In the first paragraph, he evaluates this expression, giving a concrete formula for the momentum-dependence of the electric charge, an important effect of quantum field theory. Next, he dismisses other possible diagrams that could affect the value of the electric charge. Most authors would give an explicit argument that these diagrams cancel, but for Zee it is more important to make the point that this result is expected and, from the right point of view, obvious. Finally, he discusses the implications for the relative size of the charges of the electron and the proton. If the magnitudes of charges are affected by interactions, and the proton has strong interactions but the electron does not, can it make sense that the charges of the proton and the electron are exactly equal and opposite? The answer is yes, and also that this was the real point of the whole derivation. The book takes on the full range of topics covered in typical graduate course in quantum field theory, and many additional topics: magnetic monopoles, solitons
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Quantum Yang-Mills field theory
NASA Astrophysics Data System (ADS)
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Incorporation of generalized uncertainty principle into Lifshitz field theories
NASA Astrophysics Data System (ADS)
Faizal, Mir; Majumder, Barun
2015-06-01
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S.
2013-03-25
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
Comments on conformal Killing vector fields and quantum field theory
Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.
1982-10-15
We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space.
Studies on Quantum Field Theory and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Zhang, Shoucheng
This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather form a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Koenig, Robert
2015-03-01
We give restrictions on the locality-preserving unitary automorphisms U, which are protected gates, for topologically ordered systems. For arbitrary anyon models, we show that such unitaries only generate a finite group, and hence do not provide universality. For abelian anyon models, we find that the logical action of U is contained in a proper subgroup of the generalized Clifford group. In the case D(?2), which describes Kitaev's toric code, this represents a tightening of statement previously obtained within the stabilizer framework (PRL 110:170503). For non-abelian models, we find that such automorphisms are very limited: for example, there is no non-trivial gate for Fibonacci anyons. For Ising anyons, protected gates are elements of the Pauli group. These results are derived by relating such automorphisms to symmetries of the underlying anyon model: protected gates realize automorphisms of the Verlinde algebra. We additionally use the compatibility with basis changes to characterize the logical action. This is joint work with M. Beverland, F. Pastawski, J. Preskill and S. Sijher.
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
Differential cohomology and locally covariant quantum field theory
NASA Astrophysics Data System (ADS)
Becker, Christian; Schenkel, Alexander; Szabo, Richard J.
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fréchet-Lie group structure on differential cohomology groups.
Approach to non-equilibrium behaviour in quantum field theory
Kripfganz, J.; Perlt, H.
1989-05-01
We study the real-time evolution of quantum field theoretic systems in non-equilibrium situations. Results are presented for the example of scalar /lambda//phi//sup 4/ theory. The degrees of freedom are discretized by studying the system on a torus. Short-wavelength modes are integrated out to one-loop order. The long-wavelength modes considered to be the relevant degrees of freedom are treated by semiclassical phase-space methods. /copyright/ 1989 Academic Press, Inc.
Perturbative quantum field theory in the framework of the fermionic projector
Finster, Felix
2014-04-15
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
C*-algebraic scattering theory and explicitly solvable quantum field theories
NASA Astrophysics Data System (ADS)
Warchall, Henry A.
1985-06-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.
NASA Astrophysics Data System (ADS)
Goncharov, Yu. P.
This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.
Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.
Balents, Leon; Starykh, Oleg A
2016-04-29
We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Keldysh field theory for driven open quantum systems
NASA Astrophysics Data System (ADS)
Sieberer, L. M.; Buchhold, M.; Diehl, S.
2016-09-01
Recent experimental developments in diverse areas—ranging from cold atomic gases to light-driven semiconductors to microcavity arrays—move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Quantum Corrections and Effective Action in Field Theory
NASA Astrophysics Data System (ADS)
Dalvit, Diego A. R.
1998-07-01
In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We introduce a coarse grained effective action, which is useful in the study of phase transitions in field theory. We derive an exact renormalization group equation that describes how this action varies with the coarse graining scale. We develop different approximation methods to solve that equation, and we obtain non perturbative improvements to the effective potential for a self interacting scalar field theory. We also discuss the stochastic aspects contained in this action. On the other hand, using the effective action, we find low energy and large distance quantum corrections for the gravitational potential, treating relativity as an effective low energy theory. We include the effect of scalar fields, fermions and gravitons. The inclusion of metric fluctuations causes Einstein semiclassical equations to depend on the gauge fixing parameters, and they are therefore non physical. We solve this problem identifying as a physical observable the trayectory of a test particle. We explicitly show that the geodesic equation for such particle is independent of the arbitrary parameters of the gauge fixing.
Topics in brane world and quantum field theory
NASA Astrophysics Data System (ADS)
Corradini, Olindo
In the first part of the thesis we study various issues in the Brane World scenario with particular emphasis on gravity and the cosmological constant problem. First, we study localization of gravity on smooth domain-wall solutions of gravity coupled to a scalar field. In this context we discuss how the aforementioned localization is affected by including higher curvature terms in the theory, pointing out among other things that, general combinations of such terms lead to delocalization of gravity with the only exception of the Gauss-Bonnet combination (and its higher dimensional counterparts). We then find a solitonic 3-brane solution in 6D bulk in the Einstein-Hilbert-Gauss-Bonnet theory of gravity. Near to the brane the metric is that for a product of the 4D flat Minkowski space with a 2D wedge whose deficit angle is proportional to the brane tension. Consistency tests imposed on such backgrounds appear to require the localized matter on the brane to be conformal. We then move onto infinite volume extra dimension Brane World scenarios where we study gravity in a codimension-2 model, generalizing the work of Dvali, Gabadadze and Porrati to tensionful branes. We point out that, in the presence of the bulk Gauss-Bonnet combination, the Einstein-Hilbert term is induced on the brane already at the classical level. Consistency tests are presented here as well. To conclude we discuss, using String Theory, an interesting class of large-N gauge theories which have vanishing energy density even though these theories are non-covariant and non-supersymmetric. In the second part of the thesis we study a formulation of Quantum Mechanical Path Integrals in curved space. Such Path Integrals present superficial divergences which need to be regulated. We perform a three-loop calculation in mode regularization as a nontrivial check of the non-covariant counterterms required by such scheme. We discover that dimensional regularization can be successfully adopted to evaluate the
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2015-10-01
These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.
Topics in topological and holomorphic quantum field theory
NASA Astrophysics Data System (ADS)
Vyas, Ketan
We investigate topological quantum field theories (TQFTs) in two, three, and four dimensions, as well as holomorphic quantum field theories (HQFTs) in four dimensions. After a brief overview of the two-dimensional (gauged) A and B models and the corresponding the category of branes, we construct analogous three-dimensional (gauged) A and B models and discuss the two-category of boundary conditions. Compactification allows us to identify the category of line operators in the three-dimensional A and B models with the category of branes in the corresponding two-dimensional A and B models. Furthermore, we use compactification to identify the two-category of surface operators in the four-dimensional GL theory at t = 1 and t = i with the two-category of boundary conditions in the corresponding three-dimensional A and B model, respectively. We construct a four-dimensional HQFT related to N = 1 supersymmetric quantum chromodynamics (SQCD) with gauge group SU(2) and two flavors, as well as a four-dimensional HQFT related to the Seiberg dual chiral model. On closed K ̈ahler surfaces with h^(2,0) > 0, we show that the correlation functions of holomorphic SQCD formally compute certain Donaldson invariants. For simply-connected elliptic surfaces (and their blow-ups), we show that the corresponding correlation functions in the holomorphic chiral model explicitly compute these Donaldson invariants.
Quench echo and work statistics in integrable quantum field theories.
Pálmai, T; Sotiriadis, S
2014-11-01
We propose a boundary thermodynamic Bethe ansatz calculation technique to obtain the Loschmidt echo and the statistics of the work done when a global quantum quench is performed on an integrable quantum field theory. We derive an analytic expression for the lowest edge of the probability density function and find that it exhibits universal features, in the sense that its scaling form depends only on the statistics of excitations. We perform numerical calculations on the sinh-Gordon model, a deformation of the free boson theory, and we obtain that by turning on the interaction the density function develops fermionic properties. The calculations are facilitated by a previously unnoticed property of the thermodynamic Bethe ansatz construction.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories.
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F
2017-03-10
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS_{6}×S^{2} warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p,q) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F.
2017-03-01
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6×S2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p ,q ) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Quantum Bayesianism as the basis of general theory of decision-making.
Khrennikov, Andrei
2016-05-28
We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability-one the basic laws of classical probability theory.
Preheating in an asymptotically safe quantum field theory
NASA Astrophysics Data System (ADS)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-10-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance instability in the production of these fields, and the danger that the induced curvature fluctuations will become too large. Here we show that the parametric instability indeed arises, and that hence the energy transfer from the inflaton condensate to fluctuating fields is rapid. Demanding that the curvature fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e -foldings of the inflationary phase.
NASA Astrophysics Data System (ADS)
Umezawa, H.
Throughout the course of its development in the past four decades quantum field theory has gradually acquired a very rich structure (much richer in fact than it was originally intended) and now provides us with an effective method in the analysis of many diverse areas of physics; condensed matter physics, high energy particle physics general relativity and cosmology are among the more notable examples. Since condensed matter physics deals with those phenomena in which a system of quanta exist together with a variety of macroscopic objects at finite temperature, it may be said to manifest the fundamental properties of quantum field theory in its widest sense. Thus condensed matter physics has served as a powerful motivating force throughout the growth and development of quantum field theory. This process was indeed initiated by the celebrated Matsubara formalism of finite temperature Green's function method. This process is by no means complete since recent developments in many areas of physics demand a more sophisticated understanding with regard to the fundamental nature of quantum field theory. A brief description of this maturing process of quantum field theory in the past, present and prospects for the future will be the main content of this article.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.
LETTER TO THE EDITOR: Quantum field theory and phylogenetic branching
NASA Astrophysics Data System (ADS)
Jarvis, P. D.; Bashford, J. D.
2001-12-01
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching events. The spatial dimension L is the number of leaves of the evolutionary tree under consideration. Momentum conservation modulo ←1 scattering corresponds to tree edge labelling using binary L-vectors. The bilocal quadratic term allows for momentum-dependent rate constants - only the tree or trees compatible with selected nonzero edge rates contribute to the branching probability distribution. Applications to models of evolutionary branching processes are discussed.
Quark-gluon plasma and topological quantum field theory
NASA Astrophysics Data System (ADS)
Luo, M. J.
2017-03-01
Based on an analogy with topologically ordered new state of matter in condensed matter systems, we propose a low energy effective field theory for a parity conserving liquid-like quark-gluon plasma (QGP) around critical temperature in quantum chromodynamics (QCD) system. It shows that below a QCD gap which is expected several times of the critical temperature, the QGP behaves like topological fluid. Many exotic phenomena of QGP near the critical temperature discovered at Relativistic Heavy Ion Collision (RHIC) are more readily understood by the suggestion that QGP is a topologically ordered state.
The Quantum Field Theory of the Ensemble Operator
Porter, Richard N.
2009-03-09
Quantum field theory (QFT) provides a systematic investigative tool for ensembles of molecules. The grand-canonical ensemble operator (GCEO) for an ideal gas is presented in terms of the Fock creation and annihilation operators. The ideal GCEO can be shown to obey a simple equation which facilitates calculation of quantum-statistical properties of bosonic and fermionic molecules. Examples are linked-cluster QFT derivations of the grand-canonical partition function and the Poisson distribution for non-interacting molecules. The Boltzmann limit is achieved by omitting exchange diagrams. Summations of Feynman diagrams for long- and short-range interactions to infinite order lead to a useful model of the pair-correlation function and a new avenue for the study of dynamics near the critical point for gas-liquid phase transitions.
Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices
NASA Astrophysics Data System (ADS)
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
2016-10-01
We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.
FKG inequality for the Yukawa/sub 2/ quantum field theory
Battle, G.A.; Rosen, L.
1980-02-01
WE establish the FKG correlation inequality for the Euclidean scalar Yukawa/sub 2/ quantum field model and, when the Fermi mass is zero, for pseudoscalar Yukawa/sub 2/. To do so we approximate the quantum field model by a lattice spin system and show that the FKG inequality for this system follows from a positivity condition on the fundamental solution of the Euclidean Dirac equation with external field. We prove this positivity condition by applying the Vekua--Bers theory of generalized analytic functions.
Group field theory as the second quantization of loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2016-04-01
We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the group field theory (GFT) formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
Universal behavior after a quantum quench in interacting field theories
NASA Astrophysics Data System (ADS)
Mitra, Aditi
The dynamics of an isolated quantum system represented by a field theory with O(N) symmetry, and in d>2 spatial dimensions, is investigated after a quantum quench from a disordered initial state to the critical point. A perturbative renormalization-group approach involving an expansion around d=4 is employed to study the time-evolution, and is supplemented by an exact solution of the Hartree-Fock equations in the large-N limit. The results show that the dynamics is characterized by a prethermal regime controlled by elastic dephasing where excitations propagate ballistically, and a light cone emerges in correlation functions in real space. The memory of the initial state, together with the absence of time-scales at the critical point, gives rise to universal power-law aging which is characterized by a new non-equilibrium short-time exponent. The dynamics of the entanglement following a quench is also explored, and reveals that while the time evolution of the entanglement entropy itself is not much different between a free bosonic theory and an interacting bosonic theory, the low-energy entanglement spectrum on the other hand shows clear signature of the non-equilibrium short-time exponent related to aging. This work was done in collaboration with Y. Lemonik (NYU), M. Tavora (NYU), A. Chiocchetta (SISSA), A. Maraga (SISSA), and A. Gambassi (SISSA). Supported by NSF-DMR 1303177.
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Quantum field theory with a preferred direction: The very special relativity framework
NASA Astrophysics Data System (ADS)
Lee, Cheng-Yang
2016-02-01
The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group I S I M (2 ), we present a rigorous construction of quantum field theory with a preferred direction. We find that although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations, respectively. This result can be generalized to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarized processes but are otherwise absent.
The ontology of quantum field theory: Structural realism vindicated?
Glick, David
2016-10-01
In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed theories in science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Quantum Monte Carlo calculations with chiral effective field theory interactions.
Gezerlis, A; Tews, I; Epelbaum, E; Gandolfi, S; Hebeler, K; Nogga, A; Schwenk, A
2013-07-19
We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.
(Studies in quantum field theory: Progress report, April 1, 1991--March 31, 1992)
Bender, C M
1992-01-01
Professors Bender, Bernard, and Shrauner, Assistant Professors Ogilvie and Goltermann, Research Assistant Professors Visser and Petcher, and Research Associate Rivas are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: lattice gauge calculations of masses and weak matrix elements; strong-coupling approximation; low-energy effective field theories; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; the nature of perturbation theory in large order; quark condensation in QCD; chiral fermion theories on the lattice; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD; studies of the early universe and inflation; quantum gravity. This work is described in detail in the body of this proposal.
Electromagnetic Form Factors of Hadrons in Quantum Field Theories
Dominguez, C. A.
2008-10-13
In this talk, recent results are presented of calculations of electromagnetic form factors of hadrons in the framework of two quantum field theories (QFT), (a) Dual-Large N{sub c} QCD (Dual-QCD{sub {infinity}}) for the pion, proton, and {delta}(1236), and (b) the Kroll-Lee-Zumino (KLZ) fully renormalizable Abelian QFT for the pion form factor. Both theories provide a QFT platform to improve on naive (tree-level) Vector Meson Dominance (VMD). Dual-QCD{sub {infinity}} provides a tree-level improvement by incorporating an infinite number of zero-width resonances, which can be subsequently shifted from the real axis to account for the time-like behaviour of the form factors. The renormalizable KLZ model provides a QFT improvement of VMD in the framework of perturbation theory. Due to the relative mildness of the {rho}{pi}{pi} coupling, and the size of loop suppression factors, the perturbative expansion is well defined in spite of this being a strong coupling theory. Both approaches lead to considerable improvements of VMD predictions for electromagnetic form factors, in excellent agreement with data.
Flat connection, conformal field theory and quantum group
Kato, Mitsuhiro.
1989-07-01
General framework of linear first order differential equation for four-point conformal block is studied by using flat connection. Integrability and SL{sub 2} invariance restrict possible form of flat connection. Under a special ansatz classical Yang-Baxter equation appears as an integrability condition and the WZW model turns to be unique conformal field theory in that case. Monodromy property of conformal block can be easily determined by the flat connection. 11 refs.
Derivation of anomalous hydrodynamics from quantum field theory
NASA Astrophysics Data System (ADS)
Hongo, Masaru; Hayata, Tomoya; Hidaka, Yoshimasa; Minami, Yuki; Noumi, Toshifumi
2014-09-01
Hydrodynamics is a low-energy effective theory which describes a long-distance and long-time behavior of many-body systems. It has been recently pointed out that triangle anomalies affect macroscopic transport properties and generate anomaly-induced transports. These transport phenomena have a common feature that they are dissipationless, or in other words, they don't cause the entropy production. One example is the chiral magnetic effect, which represents the existence of a dissipationless vector current along the magnetic field and is expected to occur in ultra-relativistic heavy ion collisions. In this study, we derive anomalous hydrodynamic equations from the point of view of quantum field theory. Assuming the local Gibbs distribution at initial time, we derive a thermodynamic potential for relativistic hydrodynamics. This action has a form in the curved space-time whose metric is determined by the thermodynamic variables such as the temperature. We show that anomaly-induced transports manifest from this thermodynamic potential if systems do not have the parity symmetry, and, therefore, are dissipationless. We also discuss a relation between our work and other recent approaches that aim at deriving hydrodynamic equations for the parity-violating systems. Hydrodynamics is a low-energy effective theory which describes a long-distance and long-time behavior of many-body systems. It has been recently pointed out that triangle anomalies affect macroscopic transport properties and generate anomaly-induced transports. These transport phenomena have a common feature that they are dissipationless, or in other words, they don't cause the entropy production. One example is the chiral magnetic effect, which represents the existence of a dissipationless vector current along the magnetic field and is expected to occur in ultra-relativistic heavy ion collisions. In this study, we derive anomalous hydrodynamic equations from the point of view of quantum field theory. Assuming
Decoherence and thermalization of a pure quantum state in quantum field theory.
Giraud, Alexandre; Serreau, Julien
2010-06-11
We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.
Reality, measurement and locality in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Tommasini, Daniele
2002-07-01
It is currently believed that the local causality of Quantum Field Theory (QFT) is destroyed by the measurement process. This belief is also based on the Einstein-Podolsky-Rosen (EPR) paradox and on the so-called Bell's theorem, that are thought to prove the existence of a mysterious, instantaneous action between distant measurements. However, I have shown recently that the EPR argument is removed, in an interpretation-independent way, by taking into account the fact that the Standard Model of Particle Physics prevents the production of entangled states with a definite number of particles. This result is used here to argue in favor of a statistical interpretation of QFT and to show that it allows for a full reconciliation with locality and causality. Within such an interpretation, as Ballentine and Jarret pointed out long ago, Bell's theorem does not demonstrate any nonlocality.
Plimak, L.I.; Fleischhauer, M.; Olsen, M.K.; Collett, M.J.
2003-01-01
We present an introduction to phase-space techniques (PST) based on a quantum-field-theoretical (QFT) approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation (even after phase-space doubling) and hence fail to produce a stochastic differential equation (SDE), we show how the system in question may be approximated via stochastic difference equations (S{delta}E). Second, we show that introducing sources into the SDE's (or S{delta}E's) generalizes them to a full quantum nonlinear stochastic response problem (thus generalizing Kubo's linear reaction theory to a quantum nonlinear stochastic response theory). Third, we establish general relations linking quantum response properties of the system in question to averages of operator products ordered in a way different from time normal. This extends PST to a much wider assemblage of operator products than are usually considered in phase-space approaches. In all cases, our approach yields a very simple and straightforward way of deriving stochastic equations in phase space.
Quantum revivals in conformal field theories in higher dimensions
NASA Astrophysics Data System (ADS)
Cardy, John
2016-10-01
We investigate the behavior of the return amplitude { F }(t)=| < {{\\Psi }}(0)| {{\\Psi }}(t)> | following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension d-1 and linear size O(L), from a state | {{\\Psi }}(0)> of extensive energy with short-range correlations. After an initial gaussian decay { F }(t) reaches a plateau value related to the density of available states at the initial energy. However for d=3,4 this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least O({σ }1/(d-1)L), where σ \\gg 1 is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times t˜ {{integer}}× L. In particular, on a sphere {S}d-1 of circumference 2π L, there is an action of the modular group on { F }(t) implying structure near all rational values of t/L, similar to what happens for rational CFTs in d=2.
Quantum field theory of polyelectrolyte-counterion condensation
NASA Astrophysics Data System (ADS)
Dewey, T. G.
1988-10-01
A simple quantum theory of polyelectrolyte-counterion interactions is presented. A model Hamiltonian is employed which describes both the polyelectrolyte and the counterion as free, spinless fermions. This Hamiltonian is transformed into a form which is isomorphous with traditional Hamiltonians used to describe phase transitions. The difference between this theory and early theories of superconductivity is that the counterion-counterion interaction energies will be quite large and will persist at high temperatures. The counterion condensate is a collective mode resulting from polyelectrolyte-mediated polarizations. Colligative properties for this model are compared with the Poisson-Boltzmann theory and to Manning's condensation theory.
a Unified Formalism of Thermal Quantum Field Theory
NASA Astrophysics Data System (ADS)
Chu, H.; Umezawa, H.
We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.
Double metric, generalized metric, and α' -deformed double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2016-03-01
We relate the unconstrained "double metric" of the "α' -geometry" formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b -field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application, we prove that, to first order in α' and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in α' the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.
Smooth and fast versus instantaneous quenches in quantum field theory
NASA Astrophysics Data System (ADS)
Das, Sumit R.; Galante, Damián A.; Myers, Robert C.
2015-08-01
We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale δ t, and instantaneous quenches, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies [1, 2] highlighted that the two protocols remain distinct in the limit δ t → 0 because of the relation of the quench rate to the UV cut-off, i.e., 1 /δ t ≪ Λ always holds in the fast smooth quenches while 1 /δ t ˜ Λ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small δ t, the correlator scales universally with δ t, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on δ t drops out. The excess energy density is finite (for finite mδ t) and scales in a universal fashion for all d. However, the scaling behaviour produces a divergent result in the limit mδ t → 0 for d ≥ 4, just as in an instantaneous quench, where it is UV divergent for d ≥ 4. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions Δ > d/2.
Computational approach for calculating bound states in quantum field theory
NASA Astrophysics Data System (ADS)
Lv, Q. Z.; Norris, S.; Brennan, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-09-01
We propose a nonperturbative approach to calculate bound-state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening.
Chapter 10 Quantum Mechanics and the Special and General Theory of Relativity
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered. A first principles relativistically invariant theory will be provided through a model, which is basically quantum mechanical. Moreover, by analytically extending quantum mechanics into the complex plane, it is possible to include dynamical features such as time-, length-, and temperature-scales into the theory. The flexibility of including complex symmetric interactions will in the same way support a transition from firmly quantum mechanical non-local behaviour to a decidedly classical-local appearance. Furthermore, the extended formulation gives rise to so-called Jordan blocks. They will be shown to appear logically in the present generalized dynamical picture and a compelling interpretation is microscopic self-organization (MSO). Not only have the manifestation of quantum-thermal correlations, and the emergence of generic time scales been established, but the present viewpoint also appears to throw new light on the age-old problem of quantum mechanics versus relativity. To bring all these ideas together, we will demonstrate that our model (i) displays the simple occurrence of such a degenerate unit, (ii) demonstrates the link with the Klein-Gordon-Dirac relativistic theory and (iii) provides dynamical features of both special and general relativity theory.
Quantum Theory of a Strongly-Dissipative Scalar Field
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
2017-04-01
The properties of a quantum dissipative scalar field is analyzed by Caldeira-Leggett model in strong-coupling regime. The Lagrangian of the total system is canonically quantized and the full Hamiltonian is diagonalized using Fano technique. A mode-dependent probability density is introduced. The steady state energy and correlation functions at finite temperature are calculated in terms of the probability density.
Global analysis of duality maps in quantum field theory
Restuccia, A.
1997-03-15
A global analysis of duality transformations is presented. Global constraints are introduced in order to have the correct structure of the configuration spaces. This global structure is completely determined from the quantum equivalence of dual actions. Applications to S-dual actions and to T duality of string theories and D-branes are briefly discussed. It is shown that a new topological term in the dual open string actions is required.
On truncated generalized Gibbs ensembles in the Ising field theory
NASA Astrophysics Data System (ADS)
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2017-01-01
We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green’s function G(x)=< {{\\psi}\\dagger}(x)\\psi (0)> of the complex fermion field \\psi (x) . We find that both truncated GGEs are able to recover G(x), but for a given number of charges the semi-local version performs better.
Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories
NASA Astrophysics Data System (ADS)
Babujian, H. M.; Karowski, M.; Tsvelik, A. M.
2017-04-01
We calculate the multipoint Green's functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z2 Ising model, sinh-Gordon model and Z3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
2011-03-04
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
A Chern-Simons effective field theory for the Pfaffian quantum Hall state
NASA Astrophysics Data System (ADS)
Fradkin, Eduardo; Nayak, Chetan; Tsvelik, Alexei; Wilczek, Frank
1998-04-01
We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2) 2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
Quantum Fields Obtained from Convoluted Generalized White Noise Never Have Positive Metric
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Gottschalk, Hanno
2016-05-01
It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (Lévy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from a criterion by Baumann, based on the Dell'Antonio-Robinson-Greenberg theorem, for a relativistic quantum field in positive metric to be a free field.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
NASA Astrophysics Data System (ADS)
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E.
2015-03-01
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Quantum Field Theory Tools:. a Mechanism of Mass Generation of Gauge Fields
NASA Astrophysics Data System (ADS)
Flores-Baez, F. V.; Godina-Nava, J. J.; Ordaz-Hernandez, G.
We present a simple mechanism for mass generation of gauge fields for the Yang-Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang-Mills theories without Higgs bosons.
Renormalization and non-linear symmetries in quantum field theory
NASA Astrophysics Data System (ADS)
Velenich, Andrea
Most of the phenomena we experience, from the microscopic world to the universe at its largest scales, are out of equilibrium and their comprehensive formalization is one of the open problems in theoretical physics. Fluids of interacting particles cooled down or compressed quickly enough to become amorphous solids are an example of rich out-of-equilibrium systems with very slow relaxation dynamics. Even though the equilibrium phases are ordered, these systems remain trapped in glassy metastable states, with disordered microscopic structures. As a realistic model of this phenomenology, in the first part of this work I focused on a field theory of particles obeying a Brownian dynamics. The field-theoretic action displays a time-reversal symmetry leading to Fluctuation-Dissipation relations. For non-interacting particles I solved the field theory exactly, providing the explicit form of all the correlation functions, with their space and time dependence. As a non-perturbative result, the distribution of the density field has been proven to be Poissonian and not Gaussian. For interacting particles the field theory presents two major challenges: its apparent non-renormalizability and a non-linear implementation of the time-reversal symmetry. Non-linear field redefinitions can be used to make the symmetry linear and might even lead to the solution of the interacting equations of motion. However they also alter the renormalizability properties of a field theory. These challenges inspired the second part of the work, where a more abstract approach was taken. Using algebraic methods I investigated the effect of non-linear field redefinitions both on symmetry and on renormalization by focusing on simple scalar field theories as toy models. In the formal setting of the Hopf algebra of Feynman diagrams, symmetries take the form of Hopf ideals and enforce relations among scattering amplitudes; such relations can drastically reduce the number of independent couplings in a field
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Relativistic Quantum Information Theory
2007-11-20
In S. Kalara and D.V. Nanopou- los, editors, Proceedings of the International Symposium on Black Holes , Membranes, Wormholes and Superstrings, pages...within the gravitational field of a black hole . We outline the general theory of how the entanglement of polarized photons changes under...relativistic Lorentz transformations, and have studied quantum information transmission in the presence of a black hole . A description of the accretion of
Topological Quantum Field Theory and the Geometric Langlands Correspondence
NASA Astrophysics Data System (ADS)
Setter, Kevin
In the pioneering work of A. Kapustin and E. Witten, the geometric Langlands program of number theory was shown to be intimately related to duality of GL-twisted N = 4 super Yang-Mills theory compactified on a Riemann surface. In this thesis, we generalize Kapustin-Witten by investigating compactification of the GL-twisted theory to three dimensions on a circle (for various values of the twisting parameter t). By considering boundary conditions in the three-dimensional description, we classify codimension-two surface operators of the GL-twisted theory, generalizing those surface operators studied by S. Gukov and E. Witten. For t = i, we propose a complete description of the 2-category of surface operators in terms of module categories, and, in addition, we determine the monoidal category of line operators which includes Wilson lines as special objects. For t = 1 and t = 0, we discuss surface and line operators in the abelian case. We generalize Kapustin-Witten also by analyzing a separate twisted version of N = 4, the Vafa-Witten theory. After introducing a new four-dimensional topological gauge theory, the gauged 4d A-model, we locate the Vafa-Witten theory as a special case. Compactification of the Vafa-Witten theory on a circle and on a Riemann surface is discussed. Several novel two- and three-dimensional topological gauge theories are studied throughout the thesis and in the appendices. In work unrelated to the main thread of the thesis, we conclude by classifying codimension-one topological defects in two-dimensional sigma models with various amounts of supersymmetry.
Consistency restrictions on maximal electric-field strength in quantum field theory.
Gavrilov, S P; Gitman, D M
2008-09-26
Quantum field theory with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the mean-energy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter eET2, one can see that the leading contributions to the energy are due to the creation of particles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the above-mentioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreaction.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
Exactly solvable quantum cosmologies from two killing field reductions of general relativity
NASA Astrophysics Data System (ADS)
Husain, Viqar; Smolin, Lee
1989-11-01
An exact and, possibly, general solution to the quantum constraints is given for the sector of general relativity containing cosmological solutions with two space-like, commuting, Killing fields. The dynamics of these model space-times, which are known as Gowdy space-times, is formulated in terms of Ashtekar's new variables. The quantization is done by using the recently introduced self-dual and loop representations. On the classical phase space we find four explicit physical observables, or constants of motion, which generate a GL(2) symmetry group on the space of solutions. In the loop representations we find that a complete description of the physical state space, consisting of the simultaneous solutions to all of the constraints, is given in terms of the equivalence classes, under Diff(S1), of a pair of densities on the circle. These play the same role that the link classes play in the loop representation solution to the full 3+1 theory. An infinite dimensional algebra of physical observables is found on the physical state space, which is a GL(2) loop algebra. In addition, by freezing the local degrees of freedom of the model, we find a finite dimensional quantum system which describes a set of degenerate quantum cosmologies on T3 in which the length of one of the S1's has gone to zero, while the area of the remaining S1×S1 is quantized in units of the Planck area. The quantum kinematics of this sector of the model is identical to that of a one-plaquette SU(2) lattice gauge theory.
Bipartite entanglement entropy in massive two-dimensional quantum field theory.
Doyon, Benjamin
2009-01-23
Recently, Cardy, Castro Alvaredo, and the author obtained the first exponential correction to saturation of the bipartite entanglement entropy at large region lengths in massive two-dimensional integrable quantum field theory. It depends only on the particle content of the model, and not on the way particles scatter. Based on general analyticity arguments for form factors, we propose that this result is universal, and holds for any massive two-dimensional model (also out of integrability). We suggest a link of this result with counting pair creations far in the past.
B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki
2009-04-01
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Generality with Specificity: The Dynamic Field Theory Generalizes across Tasks and Time Scales
ERIC Educational Resources Information Center
Simmering, Vanessa R.; Spencer, John P.
2008-01-01
A central goal in cognitive and developmental science is to develop models of behavior that can generalize across both tasks and development while maintaining a commitment to detailed behavioral prediction. This paper presents tests of one such model, the Dynamic Field Theory (DFT). The DFT was originally proposed to capture delay-dependent biases…
Decoherence in an interacting quantum field theory: The vacuum case
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2010-03-15
We apply the decoherence formalism to an interacting scalar field theory. In the spirit of the decoherence literature, we consider a 'system field' and an 'environment field' that interact via a cubic coupling. We solve for the propagator of the system field, where we include the self-energy corrections due to the interaction with the environment field. In this paper, we consider an environment in the vacuum state (T=0). We show that neglecting inaccessible non-Gaussian correlators increases the entropy of the system as perceived by the observer. Moreover, we consider the effect of a changing mass of the system field in the adiabatic regime, and we find that at late times no additional entropy has been generated.
Zhang, Zhen-Lu; Huang, Yong-Chang
2014-03-15
Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system. -- Highlights: •We decompose the general gauge potential into two orthogonal parts according to general field theory. •We identify a new approach for quantizing the general singular QED system. •The results obtained are superior to those for the Lorentz gauge condition. •The theory presented solves dilemmas such as the nucleon spin crisis.
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations.
Quantum field theory and gravity in causal sets
NASA Astrophysics Data System (ADS)
Sverdlov, Roman M.
Causal set is a model of space time that allows to reconcile discreteness and manifest relativistic invariance. This is done by viewing space time as finite, partially ordered set. The elements of the set are viewed as points of space time, or events; the partial ordering between them is viewed as causal relations. It has been shown that, in discrete scenario, the information about causal relations between events can, indeed, approximate the metric. The goal of this thesis is to introduce matter fields and their Lagrangians into causal set context. This is a two step process. The first step is to re-define gauge fields, gravity, and distances in such a way that no reference to Lorentz index is made. This is done by defining gauge fields as two-point real valued functions, and gravitational field as causal structure itself. Once the above is done, Lagrangians have to be defined in a way that they don't refer to Lorentzian indices either. This is done by introducing a notion of type 1 and type 2 Lagrangian generators, coupled with respective machinery that "translates" each generator into corresponding Lagrangian. The fields that are subject to these generators are, respectively, defined as type 1 and type 2. The main difference between two kinds of fields is the prediction of different behavior in different dimensions of type 2 fields. However, despite our inability to travel to different dimensions, gravity was shown to be type 2 based on the erroneous predictions of its 4-dimensional behavior if it was viewed as type 1. However, no erroneous predictions are made if non-gravitational fields are viewed as either type 1 or type 2, thus the nature of the latter is still an open question. Finally, an attempt was made to provide interpretation of quantum mechanics that would allow to limit fluctuations of causal structure to allow some topological background. However, due to its controversial nature, it is placed in the Appendix.
Exact integrability in quantum field theory and statistical systems
NASA Astrophysics Data System (ADS)
Thacker, H. B.
1981-04-01
The properties of exactly integrable two-dimensional quantum systems are reviewed and discussed. The nature of exact integrability as a physical phenomenon and various aspects of the mathematical formalism are explored by discussing several examples, including detailed treatments of the nonlinear Schrödinger (delta-function gas) model, the massive Thirring model, and the six-vertex (ice) model. The diagonalization of a Hamiltonian by Bethe's Ansatz is illustrated for the nonlinear Schrödínger model, and the integral equation method of Lieb for obtaining the spectrum of the many-body system from periodic boundary conditions is reviewed. Similar methods are applied to the massive Thirring model, where the fermion-antifermion and bound-state spectrum are obtained explicitly by the integral equation method. After a brief review of the classical inverse scattering method, the quantum inverse method for the nonlinear Schrödinger model is introduced and shown to be an algebraization of the Bethe Ansatz technique. In the quantum inverse method, an auxiliary linear problem is used to define nonlocal operators which are functionals of the original local field on a fixed-time string of arbitrary length. The particular operators for which the string is infinitely long (free boundary conditions) or forms a closed loop around a cylinder (periodic boundary conditions) correspond to the quantized scattering data and have a special significance. One of them creates the Bethe eigenstates, while the other is the generating function for an infinite number of conservation laws. The analogous operators on a lattice are constructed for the symmetric six-vertex model, where the object which corresponds to a solution of the auxiliary linear problem is a string of vertices contracted over horizontal links (arrows). The relationship between the quantum inverse method and the transfer matrix formalism is exhibited. The inverse Gel'fand-Levitan transform which expresses the local field
NASA Astrophysics Data System (ADS)
Gilmore, James Brian
2010-12-01
General Relativity is the standard framework by which all gravitational systems are analyzed in modern research, and it provides the theme for all the investigations in this thesis. Beyond this common platform, very different gravitating problems are examined here, and several analytical approaches are used to investigate these systems. Effective field theory, a methodological approach prominent in quantum field theory, plays an important role in the analysis of two of the problems in this thesis. In the first instance, an effective field theory for bound gravitational states is used to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. A metric parametrization based on a temporal Kaluza-Klein decomposition is also used. In this effective field theory calculation, the post-Newtonian results for the equations of motion are elegantly reproduced. In the next problem considered, effective field theory is used to investigate the thermodynamics of compactified charged black holes. The relevant thermodynamic quantities are all computed to second order in the perturbation parameter and finite size effects are incorporated through higher order worldline operators. Complete agreement is found with an exact extremal black hole solution constructed with traditional General Relativistic methods. The results indicate that the addition of charge to a compactified black hole may delay the phase transition to a black string. Finally, the third problem examined here concerns the evolution of perturbations at the end of early universe inflation. General Relativity enters this problem through cosmological perturbation theory. It is shown that the coherent oscillations in the inflaton break down at the comoving post-inflationary horizon size, about 14 e-folds after the end of inflation. This is many e-folds before any known constraints, leading to possible implications for the matching problem of inflation, and the generation of stochastic
Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds
NASA Astrophysics Data System (ADS)
Zois, I. P.
2016-08-01
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry.
Higher spin approaches to quantum field theory and (psuedo)-Riemannian geometries
NASA Astrophysics Data System (ADS)
Hallowell, Karl Evan
In this thesis, we study a number of higher spin quantum field theories and some of their algebraic and geometric consequences. These theories apply mostly either over constant curvature or more generally symmetric pseudo-Riemannian manifolds. The first part of this dissertation covers a superalgebra coming from a family of particle models over symmetric spaces. These theories are novel in that the symmetries of the (super)algebra osp( Q|2p) are larger and more elaborate than traditional symmetries. We construct useful (super)algebras related to and generalizing old work by Lichnerowicz and describe their role in developing the geometry of massless models with osp(Q|2 p) symmetry. The result is two practical applications of these (super)algebras: (1) a lunch more concise description of a family of higher spin quantum field theories; and (2) an interesting algebraic probe of underlying background geometries. We also consider massive models over constant curvature spaces. We use a radial dimensional reduction process which converts massless models into massive ones over a lower dimensional space. In our case, we take from the family of theories above the particular free, massless model over flat space associated with sp(2, R ) and derive a massive model. In the process, we develop a novel associative algebra, which is a deformation of the original differential operator algebra associated with the sp(2, R ) model. This algebra is interesting in its own right since its operators realize the representation structure of the sp(2, R ) group. The massive model also has implications for a sequence of unusual, "partially massless" theories. The derivation illuminates how reduced degrees of freedom become manifest in these particular models. Finally, we study a Yang-Mills model using an on-shell Poincare Yang-Mills twist of the Maxwell complex along with a non-minimal coupling. This is a special, higher spin case of a quantum field theory called a Yang-Mills detour complex
Einstein-aether theory with a Maxwell field: General formalism
Balakin, Alexander B.; Lemos, José P.S.
2014-11-15
We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.
Conformal field theory approach to Abelian and non-Abelian quantum Hall quasielectrons.
Hansson, T H; Hermanns, M; Regnault, N; Viefers, S
2009-04-24
The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
Does there exist a sensible quantum theory of an ``algebra-valued'' scalar field\\?
NASA Astrophysics Data System (ADS)
Anco, Stephen C.; Wald, Robert M.
1989-04-01
Consider a scalar field φ in Minkowski spacetime, but let φ be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincaré group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a λφ4 field, with φ valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v2=0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincaré group, is evaded here because the finite ``extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail. Thus, although the classical theory is perfectly well behaved, it seems that there does not exist a sensible quantum theory of an algebra-valued scalar field.
Objective realism and freedom of choice in relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Bednorz, Adam
2016-10-01
Traditional Bell's argument shows that freedom of choice is inconsistent with quantum realism if lack of signaling and sufficiently fast choices and readouts are assumed. While no-signaling alone is a consequence of special relativity, this is not the case of spacetime location of choice and readout. Here we attempt to incorporate freedom of choice into quantum objective realism relying solely on relativistic quantum field theory. We conclude that this is impossible without breaking relativistic invariance and put forward the possibility of signaling faster than light, which cannot be excluded if an ultimate theory violates relativity.
Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
NASA Astrophysics Data System (ADS)
Dittrich, B.; Thiemann, T.
2006-02-01
This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein Yang Mills theory and 2 + 1 gravity. Interestingly, while Yang Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity.
NASA Astrophysics Data System (ADS)
Blair, D. G.; Buckingham, M. J.
Contents: Part A. 1. Rigorous and exact. Classical general relativity: highly non-linear behaviour. Spin, geometry and topology. Approximation methods. Exact solutions. Black hole physics. Alternative theories and torsion. 2. Quantum gravity. Critical accelerations. Quantum gravity. String theories. Cosmic strings, superstrings and supergravity. Quantum cosmology: wavefunction of the universe. Quantum cosmology. 3. Cosmology. Early cosmology and quantum field theory. Supersymmetry, multidimensional cosmology and Kaluza-Klein theory. Theoretical cosmology. Large-scale structure of the universe. Dark matter. Part B. 4. Mathematical astrophysics. Algebraic computing. Numerical relativity. Astrophysics of collapsed objects. Self gravitating systems. History of general relativity. 5. Observational astrophysics. Sources of gravitational radiation. Relativistic astrophysics. Supernovae. Observation of collapsed objects. Cosmic background. 5. Precision experiments. The fifth force. Measuring the gravitational interaction in precision space experiments. Resonant bar antennas. Laser interferometer antennas. Detection of gravitational radiation. Quantum technology for gravitational radiation detection. Precision clocks in general relativity.
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
NASA Astrophysics Data System (ADS)
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Symmetries and quantum corrections in heavy quark effective field theory
NASA Astrophysics Data System (ADS)
McIrvin, Matthew James
1997-11-01
Finite-mass corrections to the Lagrangian of heavy quark effective field theory appear in a power series in the reciprocal of the quark mass. The running of these terms' coefficients to order 1/m2 is calculated to one loop, continuously redefining the quark field to eliminate operators vanishing according to the leading- order equation of motion. Results are found to agree with other recent calculations, and with constraints implied by reparameterization invariance. Different forms for the reparameterization transformation have appeared in the literature. A field redefinition is discussed which reveals the equivalence, at the level of the S-matrix, of a large family of reparameterization transformations. To order 1/m2 in the Lagrangian, these give differing predictions only for operators vanishing by the leading- order equation of motion. A new, very straightforward proof of the reparameterization constraints, applicable to order 1/m2 but to all orders in αs, is described. The results are compared with two previously proposed versions of reparameterization invariance.
Is there a "most perfect fluid" consistent with quantum field theory?
Cohen, Thomas D
2007-07-13
It was recently conjectured that the ratio of the shear viscosity to entropy density eta/s for any fluid always exceeds [formula: see text]. A theoretical counterexample to this bound can be constructed from a nonrelativistic gas by increasing the number of species in the fluid while keeping the dynamics essentially independent of the species type. The question of whether the underlying structure of relativistic quantum field theory generically inhibits the realization of such a system and thereby preserves the possibility of a universal bound is considered here. Using rather conservative assumptions, it is shown here that a metastable gas of heavy mesons in a particular controlled regime of QCD provides a realization of the counterexample and is consistent with a well-defined underlying relativistic quantum field theory. Thus, quantum field theory appears to impose no lower bound on eta/s, at least for metastable fluids.
A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
NASA Astrophysics Data System (ADS)
Nayak, Chetan; Fradkin, Eduardo; Tsvelik, Alexei; Wilczek, Frank
1998-03-01
We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at ν=1 is an SU(2)2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chern-Simons theory with coupling constant k=2. The effective field theories for other Pfaffian states, such as the fermionic one at ν=1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
Generally covariant vs. gauge structure for conformal field theories
Campigotto, M.; Fatibene, L.
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
NASA Astrophysics Data System (ADS)
Zhang, Shi-Jiang; Pan, Hui; Wang, Hai-Long
2017-04-01
An effective quantum field theory (EQFT) graphene sheet with arbitrary one dimensional strain field is derived from a microscopic effective low energy Hamiltonian. The geometric meaning of the strain-induced complex gauge field is clarified. The optical conductivity is also investigated, and a frequency dependent optical conductivity is obtained. The actual value of interband optical conductivity along the deformed direction is C0 + C1/ω2 in spite of the particular strain fields at T=0.
Anti-de Sitter quantum field theory and the AdS-CFT correspondence
NASA Astrophysics Data System (ADS)
Moschella, U.
We give a short account of a new approach to anti-de Sitter quantum field theory that is based on the assumption of certain analyticity properties of the n-point correlation functions. We then discuss the application of this formalism to the construction of conformal field theories that are naturally obtained on the covering of the cone asymptotic to the AdS manifold, and that satisfy the axioms of Luscher and Mack.
PREFACE: Quantum Field Theory Under the Influence of External Conditions (QFEXT07)
NASA Astrophysics Data System (ADS)
Bordag, M.; Mostepanenko, V. M.
2008-04-01
This special issue contains papers reflecting talks presented at the 8th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT07), held on 17 21 September 2007, at Leipzig University. This workshop gathered 108 physicists and mathematicians working on problems which are focused on the following topics: •Casimir and van der Waals forces—progress in theory and new experiments, applications at micro- and nano-scale •Casimir effect—exact results, approximate methods and mathematical problems •Vacuum quantum effects in classical background fields—renormalization issues, singular backgrounds, applications to particle and high energy physics •Vacuum energy and gravity, vacuum energy in supersymmetric and noncommutative theories. This workshop is part of a series started in 1989 and 1992 in Leipzig by Dieter Robaschik, and continued in 1995, 1998 and 2001 in Leipzig by Michael Bordag. In 2003 this Workshop was organized by Kimball A Milton in Oklahoma, in 2005 by Emilio Elizalde in Barcelona and in 2007 it returned to Leipzig. The field of physics after which this series of workshops is named is remarkably broad. It stretches from experimental work on the measurement of dispersion forces between macroscopic bodies to quantum corrections in the presence of classical background fields. The underlying physical idea is that even in its ground state (vacuum) a quantum system responds to changes in its environment. The universality of this idea makes the field of its application so very broad. The most prominent manifestation of vacuum energy is the Casimir effect. This is, in its original formulation, the attraction between conducting planes due to the vacuum fluctuations of the electromagnetic field. In a sense, this is the long-range tail of the more general dispersion forces acting between macroscopic bodies. With the progress in nanotechnology, dispersion forces become of direct practical significance. On a more theoretical side
Padmanabhan, Hamsa; Padmanabhan, T.
2011-10-15
We discuss the nonrelativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, and attempt to highlight and clarify several subtleties. In particular, we study the following issues: (a) While the action for a relativistic free particle is invariant under the Lorentz transformation, the corresponding action for a nonrelativistic free particle is not invariant under the Galilean transformation, but picks up extra contributions at the end points. This leads to an extra phase in the nonrelativistic wave function under a Galilean transformation, which can be related to the rest energy of the particle even in the nonrelativistic limit. We show that this is closely related to the peculiar fact that the relativistic action for a free particle remains invariant even if we restrict ourselves to O(1/c{sup 2}) in implementing the Lorentz transformation. (b) We provide a brief critique of the principle of equivalence in the quantum mechanical context. In particular, we show how solutions to the generally covariant Klein-Gordon equation in a noninertial frame, which has a time-dependent acceleration, reduce to the nonrelativistic wave function in the presence of an appropriate (time-dependent) gravitational field in the c{yields}{infinity} limit, and relate this fact to the validity of the principle of equivalence in a quantum mechanical context. We also show that the extra phase acquired by the nonrelativistic wave function in an accelerated frame, actually arises from the gravitational time dilation and survives in the nonrelativistic limit. (c) While the solution of the Schroedinger equation can be given an interpretation as being the probability amplitude for a single particle, such an interpretation fails in quantum field theory. We show how, in spite of this, one can explicitly evaluate the path integral using the (nonquadratic) action for a relativistic particle (involving a square root) and
Anomalies in quantum field theory and differential geometry
Manes, J.L.
1986-04-01
Anomalies in field theory appeared first in perturbative computations involving Feynman diagrams. It is only recently that differential geometric techniques have been used to obtain the form of gauge and gravitational anomalies in a direct and simple way. This is possible because of the topological nature of the anomaly. In the first chapter of this thesis the gauged Wess-Zumino action is constructed by differential geometry methods. After reviewing the relevant techniques, an expression for the action valid in any (even) number of space-time dimensions is obtained. This expression is compared with Witten's result in four dimensions. The link between topology and the anomaly is provided by the appropriate index theorem. The index density is a supersymmetric invariant polynomial from which the anomaly and other related objects can be obtained through the use of the ''descent equations.'' A new proof of the Atiyah-Singer index theorem for the Dirac operator is presented. This proof is based on the use of a WKB approximation to evaluate the supertrace of the kernel for a supersymmetric hamiltonian. The necessary WKB techniques are developed and mechanical systems with bosonic and fermionic degrees of freedom are discussed.
Anomalies in quantum field theory and differential geometry
Manes, J.L.
1986-01-01
Anomalies in field theory appeared first in perturbative computations involving Feynman diagrams. It is only recently that differential geometric techniques have been used to obtain the form of gauge and gravitational anomalies in a direct and simple way. This is possible because of the topological nature of the anomaly. In the first chapter of this thesis the gauged Wess-Zumino action is constructed by differential geometry methods. After reviewing the relevant techniques, an expression for the action valid in any (even) number of space-time dimensions is obtained. This expression is compared with Witten's result in four dimensions. The link between topology and the anomaly is provided by the appropriate index theorem. The index density is a supersymmetric invariant polynomial from which the anomaly and other related objects can be obtained through the use of the descent equations. A new proof of the Atiyah-Singer index theorem for he Dirac operator is presented in chapter 3. This proof is based on the use of a WKB approximation to evaluate the supertrace of the kernel for a supersymmetric hamiltonian. Chapter 2, which is dedicated to the development of the necessary WKB techniques, contains also a discussion of mechanical systems with bosonic and fermionic degrees of freedom.
Generalized uncertainty principle as a consequence of the effective field theory
NASA Astrophysics Data System (ADS)
Faizal, Mir; Ali, Ahmed Farag; Nassar, Ali
2017-02-01
We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.
Nonthermal fixed points in quantum field theory beyond the weak-coupling limit
NASA Astrophysics Data System (ADS)
Berges, Jürgen; Wallisch, Benjamin
2017-02-01
Quantum systems in extreme conditions can exhibit universal behavior far from equilibrium associated to nonthermal fixed points with a wide range of topical applications from early-Universe inflaton dynamics and heavy-ion collisions to strong quenches in ultracold quantum gases. So far, most studies have relied on a mapping of the quantum dynamics onto a classical-statistical theory that can be simulated on a computer. However, the mapping is based on a weak-coupling limit, while phenomenological applications often require moderate interaction strengths. We report on the observation of nonthermal fixed points directly in quantum field theory beyond the weak-coupling limit. For the example of a relativistic scalar O (N )-symmetric quantum field theory, we numerically solve the nonequilibrium dynamics employing a 1 /N expansion to next-to-leading order, which does not rely on a small coupling parameter. Starting from two different sets of overoccupied and of strong-field initial conditions, we find that nonthermal fixed points are not restricted to parameter ranges suitable for classical-statistical simulations but extend also to couplings of order 1. While the infrared behavior is found to be insensitive to the differences in the initial conditions, we demonstrate that transport phenomena to higher momenta depend on the presence or absence of a symmetry-breaking field expectation value.
Bays, Harold
2005-05-01
Excessive fat (adiposity) and dysfunctional fat (adiposopathy) constitute the most common worldwide epidemics of our time -- and perhaps of all time. Ongoing efforts to explain how the micro (adipocyte) and macro (body organ) biologic systems interact through function and dysfunction in promoting Type 2 diabetes mellitus, hypertension and dyslipidemia are not unlike the mechanistic and philosophical thinking processes involved in reconciling the micro (quantum physics) and macro (general relativity) theories in physics. Currently, the term metabolic syndrome refers to a constellation of consequences often associated with excess body fat and is an attempt to unify the associations known to exist between the four fundamental metabolic diseases of obesity, hyperglycemia (including Type 2 diabetes mellitus), hypertension and dyslipidemia. However, the association of adiposity with these metabolic disorders is not absolute and the metabolic syndrome does not describe underlying causality, nor does the metabolic syndrome necessarily reflect any reasonably related pathophysiologic process. Just as with quantum physics, general relativity and the four fundamental forces of the universe, the lack of an adequate unifying theory of micro causality and macro consequence is unsatisfying, and in medicine, impairs the development of agents that may globally improve both obesity and obesity-related metabolic disease. Emerging scientific and clinical evidence strongly supports the novel concept that it is not adiposity alone, but rather it is adiposopathy that is the underlying cause of most cases of Type 2 diabetes mellitus, hypertension and dyslipidemia. Adiposopathy is a plausible Theory of Everything for mankind's greatest metabolic epidemics.
Curved Space Quantum Field Theory of the 1970S Elucidates Boundary Casimir Energy Today
NASA Astrophysics Data System (ADS)
Fulling, S. A.
2017-03-01
Results of investigations of the divergent vacuum energy at reflecting boundaries in quantum field theory are summarized. The boundary is modeled by a soft rapidly increasing potential barrier such as a power wall. In the model without pressure anomaly and the principle of virtual work is fulfilled.
Unitarity Bounds and RG Flows in Time Dependent Quantum Field Theory
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC
2012-04-05
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-N double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
Modern Canonical Quantum General Relativity
NASA Astrophysics Data System (ADS)
Thiemann, Thomas
2007-09-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Modern Canonical Quantum General Relativity
NASA Astrophysics Data System (ADS)
Thiemann, Thomas
2008-11-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Quantum field theory in spaces with closed time-like curves
NASA Astrophysics Data System (ADS)
Boulware, D. G.
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Does there exist a sensible quantum theory of an ''algebra-valued'' scalar field
Anco, S.C.; Wald, R.M.
1989-04-15
Consider a scalar field phi in Minkowski spacetime, but let phi be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincare group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a lambdaphi/sup 4/ field, with phi valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v/sup 2/ = 0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincare group, is evaded here because the finite ''extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail.
Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory
Vary, J. P.; Maris, P.; Honkanen, H.; Li, J.; Shirokov, A. M.; Brodsky, S. J.; Harindranath, A.
2009-12-17
Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually, we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.
Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory
Vary, J.P.; Maris, P.; Shirokov, A.M.; Honkanen, H.; li, J.; Brodsky, S.J.; Harindranath, A.; Teramond, G.F.de; /Costa Rica U.
2009-08-03
Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually,we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.
Studies in quantum information theory
NASA Astrophysics Data System (ADS)
Menicucci, Nicolas C.
potential for use as generic quantum systems over which the experimenter has exquisite control and which can be used to simulate other quantum systems and also study generic quantum phenomena. This is followed by a proposal for using a trapped ion as a time-dependent harmonic oscillator---a quantum system that is common in theoretical literature but of which few laboratory examples are known. A second project studies the way that quantum fluctuations in the vibrational state of a chain of ions influence correlations in optical measurements made on the ions. The final part looks at quantum information theory in a relativistic setting. An introduction discusses the interface between quantum information theory and relativity in general, including the nonclassical notion of entanglement and the peculiar features of curved-space quantum field theory. An original gedankenexperiment combines these ideas and examines whether entanglement---a quantum information-theoretic concept and physical resource---can be used to distinguish universes of different curvature in a situation where local measurements would show no difference. These three parts are followed by a personal (and possibly controversial) conclusion, which describes my fascination with---and ultimately my reason for pursuing---studies in quantum information theory.
General Formalism of Decision Making Based on Theory of Open Quantum Systems
NASA Astrophysics Data System (ADS)
Asano, M.; Ohya, M.; Basieva, I.; Khrennikov, A.
2013-01-01
We present the general formalism of decision making which is based on the theory of open quantum systems. A person (decision maker), say Alice, is considered as a quantum-like system, i.e., a system which information processing follows the laws of quantum information theory. To make decision, Alice interacts with a huge mental bath. Depending on context of decision making this bath can include her social environment, mass media (TV, newspapers, INTERNET), and memory. Dynamics of an ensemble of such Alices is described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We speculate that in the processes of evolution biosystems (especially human beings) designed such "mental Hamiltonians" and GKSL-operators that any solution of the corresponding GKSL-equation stabilizes to a diagonal density operator (In the basis of decision making.) This limiting density operator describes population in which all superpositions of possible decisions has already been resolved. In principle, this approach can be used for the prediction of the distribution of possible decisions in human populations.
Effective-field-theory model for the fractional quantum Hall effect
NASA Technical Reports Server (NTRS)
Zhang, S. C.; Hansson, T. H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.
NASA Astrophysics Data System (ADS)
Bastin, Ted
2009-07-01
List of participants; Preface; Part I. Introduction: 1. The function of the colloquium - editorial; 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch; Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsäcker; 4. On Bohr's views concerning the quantum theory D. Bohm; Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold; 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi; 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub; 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman; 9. Measurement theory and complex systems M. A. Garstens; Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm; 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister; 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen; 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew; Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose; 15. A note on discreteness, phase space and cohomology theory B. J. Hiley; 16. Cohomology of observations R. H. Atkin; 17. The origin of half-integral spin in a discrete physical space Ted Bastin; Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsäcker; 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge; 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post; 21. How does a particle get from A to B?; Ted Bastin; 22. Informational generalization of entropy in physics Jerome Rothstein; 23. Can life explain quantum mechanics? H. H
REVIEWS OF TOPICAL PROBLEMS: Hadron clusters and half-dressed particles in quantum field theory
NASA Astrophysics Data System (ADS)
Feĭnberg, E. L.
1980-10-01
Accelerator experiments show that multiple production of hadrons in high-energy collisions of particles involves the formation of unstable intermediate entities, which subsequently decay into the final hadrons. These entities are apparently not only the comparatively light resonances with which we are already familiar but also heavy nonresonant clusters (with a mass above 2-5 GeV). The cluster concept was introduced previously in cosmic-ray physics, under the name "fireballs". To determine what these clusters are from the standpoint of quantum field theory, a detailed and thorough analysis is made of some analogous processes in quantum electrodynamics which are amenable to calculation. The QED analogs of the nonresonant clusters are "half-dressed" electrons and heavy photons. The half-dressed electrons decay into photons and electrons and are completely observable entities, whose interaction properties distinguish them from dressed electrons. In other words, the nonresonant particles are generally off-shell particles (the excursion from the mass shell is in the timelike direction). The assumption that hadron clusters are only resonances would be equivalent to a very specialized assumption regarding the nature of the spectral function of the hadron propagator; it would be different from that in electrodynamics, where the spectral function can be calculated. Nonresonant hadron clusters thus fit naturally into hadron field theory and are nonequilibrium hadrons far from the mass shell in the timelike direction. (In certain cases, their structural distortion is of the same nature as that of a half-dressed electron, so that this term can be conventionally applied to them as well.
NASA Technical Reports Server (NTRS)
Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.
1980-01-01
This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Clothed particle representation in quantum field theory: Mass renormalization
Korda, V.Yu.; Shebeko, A.V.
2004-10-15
We consider the neutral pion and nucleon fields interacting via the pseudoscalar (PS) Yukawa-type coupling. The method of unitary clothing transformations is used to handle the so-called clothed particle representation, where the total field Hamiltonian and the three boost operators in the instant form of relativistic dynamics take on the same sparse structure in the Hilbert space of hadronic states. In this approach the mass counterterms are cancelled (at least, partly) by commutators of the generators of clothing transformations and the field interaction operator. This allows the pion and nucleon mass shifts to be expressed through the corresponding three-dimensional integrals whose integrands depend on certain covariant combinations of the relevant three-momenta. The property provides the momentum independence of mass renormalization. The present results prove to be equivalent to the results obtained by Feynman techniques.
The Evolution of Quantum Field Theory: From QED to Grand Unification
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2016-10-01
In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field theoretical model to be renormalizable were established, there were two other developments that quickly accelerated acceptance of this approach: first the Brout-Englert-Higgs mechanism, and then asymptotic freedom. Together, these gave us a complete understanding of the perturbative sector of the theory, enough to give us a detailed picture of what is now usually called the Standard Model. Crucial for this understanding were the strong indications and encouragements provided by numerous experimental findings. Subsequently, non-perturbative features of the quantum field theories were addressed, and the first proposals for completely unified quantum field theories were launched. Since the use of continuous symmetries of all sorts, together with other topics of advanced mathematics, were recognised to be of crucial importance, many new predictions were pointed out, such as the Higgs particle, supersymmetry, and baryon number violation. There are still many challenges ahead.
Quantum Field Theory of Black-Swan Events
NASA Astrophysics Data System (ADS)
Kleinert, H.
2014-05-01
Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.
Alien calculus and non perturbative effects in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
Generalized quantum kinetic expansion: Higher-order corrections to multichromophoric Förster theory.
Wu, Jianlan; Gong, Zhihao; Tang, Zhoufei
2015-08-21
For a general two-cluster energy transfer network, a new methodology of the generalized quantum kinetic expansion (GQKE) method is developed, which predicts an exact time-convolution equation for the cluster population evolution under the initial condition of the local cluster equilibrium state. The cluster-to-cluster rate kernel is expanded over the inter-cluster couplings. The lowest second-order GQKE rate recovers the multichromophoric Förster theory (MCFT) rate. The higher-order corrections to the MCFT rate are systematically included using the continued fraction resummation form, resulting in the resummed GQKE method. The reliability of the GQKE methodology is verified in two model systems, revealing the relevance of higher-order corrections.
Generalized quantum kinetic expansion: Higher-order corrections to multichromophoric Förster theory
Wu, Jianlan Gong, Zhihao; Tang, Zhoufei
2015-08-21
For a general two-cluster energy transfer network, a new methodology of the generalized quantum kinetic expansion (GQKE) method is developed, which predicts an exact time-convolution equation for the cluster population evolution under the initial condition of the local cluster equilibrium state. The cluster-to-cluster rate kernel is expanded over the inter-cluster couplings. The lowest second-order GQKE rate recovers the multichromophoric Förster theory (MCFT) rate. The higher-order corrections to the MCFT rate are systematically included using the continued fraction resummation form, resulting in the resummed GQKE method. The reliability of the GQKE methodology is verified in two model systems, revealing the relevance of higher-order corrections.
Preconjugate variables in quantum field theory and their applications
NASA Astrophysics Data System (ADS)
Much, Albert; Pottel, Steffen; Sibold, Klaus
2016-09-01
Preconjugate variables X have commutation relations with the energy-momentum P of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new spacetimes, we present a study of them here. Interesting examples X can be found via geometry—motions on the mass shell for massive and massless systems—and via group theory—invariance under special conformal transformations of the mass shell and light cone, respectively. Both find representations on Fock space. We work mainly in ordinary four-dimensional Minkowski space and spin zero. The limit process from nonzero to vanishing mass turns out to be nontrivial and leads naturally to wedge variables. We point out some applications and extensions to more general spacetimes. In a companion paper, we discuss the transition to conjugate pairs.
Thermalization and revivals after a quantum quench in conformal field theory.
Cardy, John
2014-06-06
We consider a quantum quench in a finite system of length L described by a 1+1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature β≪L. For times t such that ℓ/2
Symmetries in tetrad theories. [of gravitational fields and general relativity
NASA Technical Reports Server (NTRS)
Chinea, F. J.
1988-01-01
The isometry conditions for gravitational fields are given directly at the tetrad level, rather than in terms of the metric. As an illustration, an analysis of the curvature collineations and Killing fields for a twisting type-N vacuum gravitational field is made.
Domain walls, fusion rules, and conformal field theory in the quantum Hall regime.
Ardonne, Eddy
2009-05-08
We provide a simple way to obtain the fusion rules associated with elementary quasiholes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We show that, for a certain two-parameter family (k,r) of wave functions, the fusion rules are those of su(r)k. In addition, we give an explicit conformal field theory construction of these states, based on the Mk(k+1,k+r) "minimal" theories. For r=2, these states reduce to the Read-Rezayi states. The "Gaffnian" wave function is the prototypical example for r>2, in which case the conformal field theory is nonunitary.
Bayesian inference of nonpositive spectral functions in quantum field theory
NASA Astrophysics Data System (ADS)
Rothkopf, Alexander
2017-03-01
We present the generalization to nonpositive definite spectral functions of a recently proposed Bayesian deconvolution approach (BR method). The novel prior used here retains many of the beneficial analytic properties of the original method; in particular, it allows us to integrate out the hyperparameter α directly. To preserve the underlying axiom of scale invariance, we introduce a second default-model related function, whose role is discussed. Our reconstruction prescription is contrasted with existing direct methods, as well as with an approach where shift functions are introduced to compensate for negative spectral features. A mock spectrum analysis inspired by the study of gluon spectral functions in QCD illustrates the capabilities of this new approach.
From conformal field theory spectra to CMB multipoles in quantum gravity cosmology
Hamada, Ken-ji; Horata, Shinichi; Yukawa, Tetsuyuki
2010-04-15
We study the inflation process of the Universe based on the renormalizable quantum gravity formulated as a conformal field theory. We show that the power-law conformal field theory spectrum approaches that of the Harrison-Zel'dovich-Peebles-type as the amplitude of gravitational potential gradually reduces during the inflation. The non-Gaussanity parameter is preserved within an order of unity due to the diffeomorphism invariance. Sharp falloff of the angular power spectrum of cosmic microwave background at large scale is understood as a consequence of the existence of dynamical scale of the quantum gravity {Lambda}{sub QG}({approx_equal}10{sup 17} GeV). The angular power spectra are computed and compared with the WMAP5 and ACBAR data with a quality of {chi}{sup 2}/dof{approx_equal}1.1.
Families of particles with different masses in PT-symmetric quantum field theory.
Bender, Carl M; Klevansky, S P
2010-07-16
An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex-field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.
Space--Time from Topos Quantum Theory
NASA Astrophysics Data System (ADS)
Flori, Cecilia
One of the main challenges in theoretical physics in the past 50 years has been to define a theory of quantum gravity, i.e. a theory which consistently combines general relativity and quantum theory in order to define a theory of space-time itself seen as a fluctuating field. As such, a definition of space-time is of paramount importance, but it is precisely the attainment of such a definition which is one of the main stumbling blocks in quantum gravity. One of the striking features of quantum gravity is that although both general relativity and quantum theory treat space-time as a four-dimensional (4D) manifold equipped with a metric, quantum gravity would suggest that, at the microscopic scale, space-time is somewhat discrete. Therefore the continuum structure of space-time suggested by the two main ingredients of quantum gravity seems to be thrown into discussion by quantum gravity itself. This seems quite an odd predicament, but it might suggest that perhaps a different mathematical structure other than a smooth manifold should model space-time. These considerations seem to shed doubts on the use of the continuum in general in a possible theory of quantum gravity. An alternative would be to develop a mathematical formalism for quantum gravity in which no fundamental role is played by the continuum and where a new concept of space-time, not modeled on a differentiable manifold, will emerge. This is precisely one of the aims of the topos theory approach to quantum theory and quantum gravity put forward by Isham, Butterfield, and Doering and subsequently developed by other authors. The aim of this article is to precisely elucidate how such an approach gives rise to a new definition of space-time which might be more appropriate for quantum gravity.
Resurgence in quantum field theory: nonperturbative effects in the principal chiral model.
Cherman, Aleksey; Dorigoni, Daniele; Dunne, Gerald V; Ünsal, Mithat
2014-01-17
We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory. These points are illustrated in the PCM, where we find new nonperturbative "fracton" saddle point field configurations, and suggest a quantum interpretation of previously discovered "uniton" unstable classical solutions. The fractons lead to a semiclassical realization of IR renormalons in the circle-compactified theory and yield the microscopic mechanism of the mass gap of the PCM.
Gürdoğan, Ömer; Kazakov, Vladimir
2016-11-11
We introduce a family of new integrable quantum field theories in four dimensions by considering the γ-deformed N=4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the 't Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS/CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N=4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.
NASA Astrophysics Data System (ADS)
Gürdoǧan, Ömer; Kazakov, Vladimir
2016-11-01
We introduce a family of new integrable quantum field theories in four dimensions by considering the γ -deformed N =4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the `t Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS /CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N =4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar
2016-09-01
We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Effective field theory for the quantum electrodynamics of a graphene wire
Faccioli, P.; Lipparini, E.
2009-07-15
We study the low-energy quantum electrodynamics of electrons and holes in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/p{sub T}, where p{sub T} is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest order in (p/p{sub T}), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound states, and we calculate the dispersion law of such modes. We also compute the dc conductivity per unit length at zero chemical potential and find g{sub s}(e{sup 2}/h), where g{sub s}=4 is the degeneracy factor.
NASA Astrophysics Data System (ADS)
Bochicchio, Marco
2015-03-01
We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse-Smale-Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang-Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in (1)/(N), a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a
Universal scaling of the logarithmic negativity in massive quantum field theory
NASA Astrophysics Data System (ADS)
Blondeau-Fournier, Olivier; Castro-Alvaredo, Olalla A.; Doyon, Benjamin
2016-03-01
We consider the logarithmic negativity, a measure of bipartite entanglement, in a general unitary 1 + 1-dimensional massive quantum field theory, not necessarily integrable. We compute the negativity between a finite region of length r and an adjacent semi-infinite region, and that between two semi-infinite regions separated by a distance r. We show that the former saturates to a finite value, and that the latter tends to zero, as r\\to ∞ . We show that in both cases, the leading corrections are exponential decays in r (described by modified Bessel functions) that are solely controlled by the mass spectrum of the model, independently of its scattering matrix. This implies that, like the entanglement entropy (EE), the logarithmic negativity displays a very high level of universality, allowing one to extract information about the mass spectrum. Further, a study of sub-leading terms shows that, unlike the EE, a large-r analysis of the negativity allows for the detection of bound states.
Classical and quantum theory of the massive spin-two field
NASA Astrophysics Data System (ADS)
Koenigstein, Adrian; Giacosa, Francesco; Rischke, Dirk H.
2016-05-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers JPC =2-+ is, to our knowledge, given here for the first time.
Unification of gravity and quantum field theory from extended noncommutative geometry
NASA Astrophysics Data System (ADS)
Yu, Hefu; Ma, Bo-Qiang
2017-02-01
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.
Bound State Problems and Study of Symmetry in Quantum Field Theory.
NASA Astrophysics Data System (ADS)
Levine, Robert Yale
This dissertation has four independent parts. The first part is a study of heavy quark-antiquark bound states. After a review of early nonrelativistic potential models an analytic potential form is derived based on the quantum chromodynamic running coupling constant and the string model. Various methods of fixing parameters in the potential lead to descriptions of (psi)/J, (UPSILON) and (t(')t) resonances. Energy levels, leptonic decay and E1 transition rates are calculated. Speculations on the mass dependence of leptonic decay rates, and on effects of spin-spin interactions on leptonic decay rates, are given. In the second part a theory of positron desorption from metal surfaces is derived and applied to surface positron conversion to positronium. Angular distribution and energy dependence of positronium from Al(100) are calculated as well as the polarization of pickup electrons from ferromagnetic nickel. Part three is a study of the supersymmetry algebra resulting with commuting (not nilpotent) parameters. The extended algebra is an infinite dimensional Kac-Moody type algebra with momentum in the role of the geometrical parameter. Representations of the resulting fixed momentum finite algebra are analyzed in the massive and massless case. The Klein transformation is introduced to accommodate the generator's fermionic statistics. Field theory representations which modify the Wess-Zumino model with abnormal statistics are shown to satisfy the infinite Lie algebra. The final part is a study of generalized parastatistics motivated by the identification of the Green index with an internal symmetry index. Generalized double commutation relations are introduced which are covariant rather than invariant under internal symmetry transformations. A study is made of local invariant interaction terms and types of normal Higgs mechanisms which are allowed by generalized statistics. Symmetry transmutation, a modification of normal isospin relations due to general statistics, is
Ambiguities and subtleties in fermion mass terms in practical quantum field theory
Cheng, Yifan Kong, Otto C.W.
2014-09-15
This is a review on structure of the fermion mass terms in quantum field theory, under the perspective of its practical applications in the real physics of Nature—specifically, we discuss fermion mass structure in the Standard Model of high energy physics, which successfully describes fundamental physics up to the TeV scale. The review is meant to be pedagogical, with detailed mathematics presented beyond the level one can find any easily in the textbooks. The discussions, however, bring up important subtleties and ambiguities about the subject that may be less than well appreciated. In fact, the naive perspective of the nature and masses of fermions as one would easily drawn from the presentations of fermion fields and their equations of motion from a typical textbook on quantum field theory leads to some confusing or even wrong statements which we clarify here. In particular, we illustrate clearly that a Dirac fermion mass eigenstate is mathematically equivalent to two degenerated Majorana fermion mass eigenstates at least as long as the mass terms are concerned. There are further ambiguities and subtleties in the exact description of the eigenstate(s). Especially, for the case of neutrinos, the use of the Dirac or Majorana terminology may be mostly a matter of choice. The common usage of such terminology is rather based on the broken SU(2) charges of the related Weyl spinors hence conventional and may not be unambiguously extended to cover more complicate models. - Highlights: • Structure of fermion mass terms in practical quantum field theory is reviewed. • Important subtleties and ambiguities on the subject are clarified. • A mass eigenstate Dirac fermion and two degenerated Majorana ones are equivalent. • The conventional meaning of such terminology for neutrinos is critically discussed.
NASA Astrophysics Data System (ADS)
Griffiths, Robert B.
2001-11-01
Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
Buividovich, P. V.
2011-02-15
We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all the histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. A stochastic solution of the self-consistency conditions can be implemented as a 'memory' of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the two-dimensional O(N) sigma model. The extension to non-Abelian lattice gauge theories is discussed.
Relational evolution of effectively interacting group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi
2017-03-01
We study the impact of effective interactions onto relationally evolving group field theory (GFT) condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
NASA Astrophysics Data System (ADS)
Vian, F.
1999-05-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.
Quantum mechanics and quantum information theory
NASA Astrophysics Data System (ADS)
van Camp, Wesley William
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches -- that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism -- fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel
Chiral scale and conformal invariance in 2D quantum field theory.
Hofman, Diego M; Strominger, Andrew
2011-10-14
It is well known that a local, unitary Poincaré-invariant 2D quantum field theory with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this Letter, we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left conformal symmetry is still implied, while right translations are enhanced either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.
Friedberg, R; Hohenberg, P C
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
Continuous point symmetries in group field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2017-03-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on group field theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them.
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2014-04-01
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2014-02-01
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet
Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions
Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán
2013-01-01
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory. PMID:24790954
Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán
2013-01-01
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Ambiguities and subtleties in fermion mass terms in practical quantum field theory
NASA Astrophysics Data System (ADS)
Cheng, Yifan; Kong, Otto C. W.
2014-09-01
This is a review on structure of the fermion mass terms in quantum field theory, under the perspective of its practical applications in the real physics of Nature-specifically, we discuss fermion mass structure in the Standard Model of high energy physics, which successfully describes fundamental physics up to the TeV scale. The review is meant to be pedagogical, with detailed mathematics presented beyond the level one can find any easily in the textbooks. The discussions, however, bring up important subtleties and ambiguities about the subject that may be less than well appreciated. In fact, the naive perspective of the nature and masses of fermions as one would easily drawn from the presentations of fermion fields and their equations of motion from a typical textbook on quantum field theory leads to some confusing or even wrong statements which we clarify here. In particular, we illustrate clearly that a Dirac fermion mass eigenstate is mathematically equivalent to two degenerated Majorana fermion mass eigenstates at least as long as the mass terms are concerned. There are further ambiguities and subtleties in the exact description of the eigenstate(s). Especially, for the case of neutrinos, the use of the Dirac or Majorana terminology may be mostly a matter of choice. The common usage of such terminology is rather based on the broken SU(2) charges of the related Weyl spinors hence conventional and may not be unambiguously extended to cover more complicate models.
Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
NASA Astrophysics Data System (ADS)
Roberts, Daniel A.; Swingle, Brian
2016-08-01
As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound—the Lieb-Robinson bound—and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the "butterfly" velocity vB . Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that vB is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that vB remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.
Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories.
Roberts, Daniel A; Swingle, Brian
2016-08-26
As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound-the Lieb-Robinson bound-and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the "butterfly" velocity v_{B}. Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that v_{B} is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that v_{B} remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.
NASA Astrophysics Data System (ADS)
Buchhold, Michael; Everest, Benjamin; Marcuzzi, Matteo; Lesanovsky, Igor; Diehl, Sebastian
2017-01-01
Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave, which has proved a rather stringent requirement in experiments. Recently, a proposal to seek such transitions in highly tunable systems of cold-atomic gases offers to probe this physics and, at the same time, to investigate the robustness of these transitions to quantum coherent effects. Here, we specifically focus on the interplay between classical and quantum fluctuations in a simple driven open quantum model which, in the classical limit, reproduces a contact process, which is known to undergo a continuous transition in the "directed percolation" universality class. We derive an effective long-wavelength field theory for the present class of open spin systems and show that, due to quantum fluctuations, the nature of the transition changes from second to first order, passing through a bicritical point which appears to belong instead to the "tricritical directed percolation" class.
CP(N - 1) quantum field theories with alkaline-earth atoms in optical lattices
NASA Astrophysics Data System (ADS)
Laflamme, C.; Evans, W.; Dalmonte, M.; Gerber, U.; Mejía-Díaz, H.; Bietenholz, W.; Wiese, U.-J.; Zoller, P.
2016-07-01
We propose a cold atom implementation to attain the continuum limit of (1 + 1) -d CP(N - 1) quantum field theories. These theories share important features with (3 + 1) -d QCD, such as asymptotic freedom and θ-vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N - 1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic preparation of the ground state of the system, the real-time evolution of a false θ-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.
NASA Astrophysics Data System (ADS)
Tsapalis, Antonios S.
This thesis deals with two topics in lattice field theories. In the first part we discuss aspects of renormalization group flow and non-perturbative improvement of actions for scalar theories regularized on a lattice. We construct a perfect action, an action which is free of lattice artifacts, for a given theory. It is shown how a good approximation to the perfect action-referred to as classically perfect-can be constructed based on a well-defined blocking scheme for the O(3) non-linear σ-model. We study the O(N) non- linear σ-model in the large-N limit and derive analytically its perfect action. This action is applied to the O(3) model on a square lattice. The Wolff cluster algorithm is used to simulate numerically the system. We perform scaling tests and discuss the scaling properties of the large- N inspired perfect action as opposed to the standard and the classically perfect action. In the second part we present a new formulation for a quantum field theory with Abelian gauge symmetry. A Hamiltonian is constructed on a four-dimensional Euclidean space-time lattice which is invariant under local transformations. The model is formulated as a 5- dimensional path integral of discrete variables. We argue that dimensional reduction will allow us to study the behavior of the standard compact U(1) gauge theory in 4-d. Based on the idea of the loop- cluster algorithm for quantum spins, we present the construction of a flux-cluster algorithm for the U(1) quantum link model for the spin-1/2 quantization of the electric flux. It is shown how improved estimators for Wilson loop expectation values can be defined. This is important because the Wilson loops are traditionally used to identify confining and Coulomb phases in gauge theories. Our study indicates that the spin-1/2 U(1) quantum link model is strongly coupled for all bare coupling values we examined. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
NASA Astrophysics Data System (ADS)
Milošević, D. B.; Becker, W.
2016-06-01
A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the T -matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency ω . Special emphasis is on the ω -2 ω case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.
Quantum bound on the specific entropy in strongly coupled scalar field theory
Aparicio Alcalde, M.; Menezes, G.; Svaiter, N. F.
2008-06-15
We discuss the (g{sub 0}{phi}{sup p}){sub d} self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the field in a hypercube of side L. We also consider that the system is in thermal equilibrium at temperature {beta}{sup -1}. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E)<2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. Employing the strong-coupling perturbative expansion, we obtain the renormalized mean energy E and entropy S for the system up to the order (g{sub 0}){sup -(2/p)}, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. Defining {epsilon}{sub d}{sup (r)} as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity {xi}=({beta}/L) and h{sub 1}(d) and h{sub 2}(d) as positive analytic functions of d, for the case of high temperature, we get that the specific entropy satisfies (S/E)<2{pi}R(h{sub 1}(d)/h{sub 2}(d)){xi}. When considering the low-temperature behavior of the specific entropy, we have (S/E)<2{pi}R(h{sub 1}(d)/{epsilon}{sub d}{sup (r)}){xi}{sup 1-d}. Therefore the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero-point energy is a positive quantity, at intermediate temperatures and in the low-temperature limit, there is a quantum bound.
Interacting quantum fields and the chronometric principle
Segal, I. E.
1976-01-01
A form of interaction in quantum field theory is described that is physically intrinsic rather than superimposed via a postulated nonlinearity on a hypothetical free field. It derives from the extension to general symmetries of the distinction basic for the chronometric cosmology between the physical (driving) and the observed energies, together with general precepts of quantum field theory applicable to nonunitary representations. The resulting interacting field is covariant, causal, involves real particle production, and is devoid of nontrivial ultraviolet divergences. Possible physical applications are discussed. PMID:16592353
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K. . Inst. for Theoretical Physics); Sevrin, A. ); van Nieuwenhuizen, P. . Theory Div.)
1991-11-01
In this contribution to Tini Veltman's Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields ( the metric') are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K.; Sevrin, A.; van Nieuwenhuizen, P.
1991-11-01
In this contribution to Tini Veltman`s Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields (`the metric`) are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
The most general second-order field equations of bi-scalar-tensor theory in four dimensions
NASA Astrophysics Data System (ADS)
Ohashi, Seiju; Tanahashi, Norihiro; Kobayashi, Tsutomu; Yamaguchi, Masahide
2015-07-01
The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.
NASA Astrophysics Data System (ADS)
Steffens, A.; Riofrío, C. A.; Hübener, R.; Eisert, J.
2014-12-01
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states (cMPS), a complete set of variational states grasping states in one-dimensional quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomized cMPS from their correlation data and study the robustness of the reconstruction for different noise models. Furthermore, we apply the method to data generated by simulations based on cMPS and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as those encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.
General theory of measurement with two copies of a quantum state.
Bendersky, Ariel; Paz, Juan Pablo; Cunha, Marcelo Terra
2009-07-24
We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that mu can label a set of outcomes of a measurement on two copies if and only if there is a family of maps C_{micro} such that the probability Prob(micro) is the fidelity of each map, i.e., Prob(micro) = Tr[rhoC_{micro}(rho)]. Here, the map C_{micro} must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure).
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
Ellis, R. Keith; Kunszt, Zoltan; Melnikov, Kirill; Zanderighi, Giulia
2012-09-01
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.
Tunnelling of the 3rd kind: A test of the effective non-locality of quantum field theory
NASA Astrophysics Data System (ADS)
Gardiner, Simon A.; Gies, Holger; Jaeckel, Joerg; Wallace, Chris J.
2013-03-01
Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this letter we argue that tunnelling of the 3rd kind —where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance— provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.
From quantum Bäcklund transforms to topological quantum field theory
NASA Astrophysics Data System (ADS)
Korff, Christian
2016-03-01
We derive the quantum analogue of a Bäcklund transformation for the quantized Ablowitz-Ladik chain, a space discretization of the nonlinear Schrödinger equation. The quantization of the Ablowitz-Ladik chain leads to the q-boson model. Using a previous construction of Baxter’s Q-operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical Bäcklund transform to all orders in {\\hslash }. We construct also a second Q-operator and show that it is closely related to the inverse of the first. The multi-Bäcklund transforms generated from the Q-operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients.
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
NASA Astrophysics Data System (ADS)
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
NASA Astrophysics Data System (ADS)
Wang, Hao; Yang, Weitao
2016-06-01
We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics' force fields and nontransferable molecule-specific atomic polarizabilities.
Wang, Hao; Yang, Weitao
2016-06-14
We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics' force fields and nontransferable molecule-specific atomic polarizabilities.
Auxiliary-field quantum Monte Carlo simulations of neutron matter in chiral effective field theory.
Wlazłowski, G; Holt, J W; Moroz, S; Bulgac, A; Roche, K J
2014-10-31
We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wave function of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10(3) discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Λ=414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Λ=414 MeV [L. Coraggio et al., Phys. Rev. C 87, 014322 (2013).
Quantum Theory is an Information Theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo M.; Perinotti, Paolo
2016-03-01
In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.
Recent advances toward a general purpose linear-scaling quantum force field.
Giese, Timothy J; Huang, Ming; Chen, Haoyuan; York, Darrin M
2014-09-16
Conspectus There is need in the molecular simulation community to develop new quantum mechanical (QM) methods that can be routinely applied to the simulation of large molecular systems in complex, heterogeneous condensed phase environments. Although conventional methods, such as the hybrid quantum mechanical/molecular mechanical (QM/MM) method, are adequate for many problems, there remain other applications that demand a fully quantum mechanical approach. QM methods are generally required in applications that involve changes in electronic structure, such as when chemical bond formation or cleavage occurs, when molecules respond to one another through polarization or charge transfer, or when matter interacts with electromagnetic fields. A full QM treatment, rather than QM/MM, is necessary when these features present themselves over a wide spatial range that, in some cases, may span the entire system. Specific examples include the study of catalytic events that involve delocalized changes in chemical bonds, charge transfer, or extensive polarization of the macromolecular environment; drug discovery applications, where the wide range of nonstandard residues and protonation states are challenging to model with purely empirical MM force fields; and the interpretation of spectroscopic observables. Unfortunately, the enormous computational cost of conventional QM methods limit their practical application to small systems. Linear-scaling electronic structure methods (LSQMs) make possible the calculation of large systems but are still too computationally intensive to be applied with the degree of configurational sampling often required to make meaningful comparison with experiment. In this work, we present advances in the development of a quantum mechanical force field (QMFF) suitable for application to biological macromolecules and condensed phase simulations. QMFFs leverage the benefits provided by the LSQM and QM/MM approaches to produce a fully QM method that is able to
Mukamel, Shaul
2003-08-01
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach.
Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang
2013-02-22
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
Tests of General Theory of Relativity
NASA Astrophysics Data System (ADS)
Brynjolfsson, Ari
2002-04-01
Einstein’s theory of general relativity and experiments proving it are all in the domain of classical physics. These include experiments by Pound, Rebka, and Snider of the gravitational redshift of 14.4 keV photons; the rocket experiments by Vessot et al.; the Galileo redshift experiments by Krisher et al.; the gravitational deflection of light experiments by Riveros and Vucetich; and delay of echoes of radar signals passing close to Sun as observed by Shapiro et al. Bohr’s correspondence principle assures that the quantum mechanical theory of general relativity agrees with Einstein’s classical theory when frequency and gravitational field gradient approach zero, or when photons cannot interact with the gravitational field. Quantum theory invalidates some of the assumption made by Einstein. His argument that equally many crests of waves must arrive on Earth as leave Sun is correct in classical physics, but impermissible in quantum mechanics. We will show that solar redshift experiments contradict the classical theory and support a quantum mechanically modified theory of general relativity. This changes drastically the entire theory, including the equivalence principle.
Generalized local-frame-transformation theory for excited species in external fields
NASA Astrophysics Data System (ADS)
Giannakeas, P.; Greene, Chris H.; Robicheaux, F.
2016-07-01
A rigorous theoretical framework is developed for a generalized local-frame-transformation theory (GLFT). The GLFT is applicable to the following systems: Rydberg atoms or molecules in an electric field and negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local-frame-transformation theory developed initially by U. Fano [Phys. Rev. A 24, 619 (1981), 10.1103/PhysRevA.24.619] and D. A. Harmin [Phys. Rev. A 26, 2656 (1982), 10.1103/PhysRevA.26.2656]. This revised GLFT theory yields nontrivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semianalytical GLFT Stark spectra with ab initio numerical simulations yield errors in the range of a few tens of MHz, an improvement over the original Fano-Harmin theory, whose errors are 10-100 times larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.
NASA Astrophysics Data System (ADS)
Schroer, B.
2010-07-01
After revisiting some high points of particle physics and QFT of the two decades from 1960 to 1980, I comment on the work by Jorge André Swieca. I explain how it fits into the quantum field theory during these two decades and draw attention to its relevance to the ongoing particle physics research. A particular aim of this article is to direct the readers mindfulness to the relevance of what at the time of Swieca was called “the Schwinger Higgs screening mechanism” which, together with recent ideas which generalize the concept of gauge theories, has all the ingredients to revolutionize the issue of gauge theories and the standard model.
Effective field theory and non-Gaussianity from general inflationary states
NASA Astrophysics Data System (ADS)
Agarwal, Nishant; Holman, R.; Tolley, Andrew J.; Lin, Jennifer
2013-05-01
We study the effects of non-trivial initial quantum states for inflationary fluctuations within the context of the effective field theory for inflation constructed by Cheung et al. which allows us to discriminate between different initial states in a model-independent way. We develop a Green's function/path integral based formulation that incorporates initial state effects and use it to address questions such as how state-dependent is the consistency relation for the bispectrum, how many e-folds beyond the minimum required to solve the cosmological fine tunings of the big bang are we allowed so that some information from the initial state survives until late times, among others. We find that the so-called consistency condition relating the local limit of the bispectrum and the slow-roll parameter is a state-dependent statement that can be avoided for physically consistent initial states either with or without initial non-Gaussianities.
Generalized scale invariant theories
NASA Astrophysics Data System (ADS)
Padilla, Antonio; Stefanyszyn, David; Tsoukalas, Minas
2014-03-01
We present the most general actions of a single scalar field and two scalar fields coupled to gravity, consistent with second-order field equations in four dimensions, possessing local scale invariance. We apply two different methods to arrive at our results. One method, Ricci gauging, was known to the literature and we find this to produce the same result for the case of one scalar field as a more efficient method presented here. However, we also find our more efficient method to be much more general when we consider two scalar fields. Locally scale invariant actions are also presented for theories with more than two scalar fields coupled to gravity and we explain how one could construct the most general actions for any number of scalar fields. Our generalized scale invariant actions have obvious applications to early Universe cosmology and include, for example, the Bezrukov-Shaposhnikov action as a subset.
Quantum field theory and classical optics: determining the fine structure constant
NASA Astrophysics Data System (ADS)
Leuchs, Gerd; Hawton, Margaret; Sánchez-Soto, Luis L.
2017-01-01
The properties of the vacuum are described by quantum physics including the response to external fields such as electromagnetic radiation. Of the two parameters that govern the details of the electromagnetic field dynamics in vacuum, one is fixed by the requirement of Lorentz invariance c = 1/\\sqrt {ε 0 μ 0 } . The other one, Z0 = \\sqrt {μ 0 /ε 0 } = 1/(cε 0 ) and its relation to the quantum vacuum, is discussed in this contribution. Deriving ε 0 from the properties of the quantum vacuum implies the derivation of the fine structure constant.
NASA Astrophysics Data System (ADS)
Haldane, F. D. M.; Ha, Z. N. C.; Talstra, J. C.; Bernard, D.; Pasquier, V.
1992-10-01
The SU(n) quantum chains with inverse-square exchange exhibit a novel form of Yangian symmetry compatible with periodic boundary conditions, allowing states to be countable. We characterize the ``supermultiplets'' of the spectrum in terms of generalized ``occupation numbers.'' We embed the model in the k=1 SU(n) Kac-Moody algebra and obtain a new classification of the states of conformal field theory, adapted to particlelike elementary excitations obeying fractional statistics.
Donchev, A. G.; Galkin, N. G.; Illarionov, A. A.; Khoruzhii, O. V.; Olevanov, M. A.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, V. I.
2006-01-01
We have recently introduced a quantum mechanical polarizable force field (QMPFF) fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here, we present an improved form of the force field, QMPFF2, and apply it to simulations of liquid water. The results of the simulations show excellent agreement with a variety of experimental thermodynamic and structural data, as good or better than that provided by specialized water potentials. In particular, QMPFF2 is the only ab initio force field to accurately reproduce the anomalous temperature dependence of water density to our knowledge. The ability of the same force field to successfully simulate the properties of both organic molecules and water suggests it will be useful for simulations of proteins and protein–ligand interactions in the aqueous environment. PMID:16723394
Quantum theory of measurements as quantum decision theory
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2015-03-01
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device.
NASA Technical Reports Server (NTRS)
Li, Xi-Zeng; Su, Bao-Xia
1994-01-01
It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.
NASA Astrophysics Data System (ADS)
Friedan, Daniel
2010-03-01
An abstract argument is offered that the ideal physical systems for asymptotically large-scale quantum computers are near-critical quantum circuits, critical in the bulk, whose bulk universality classes are described by 1+1d conformal field theories. One in particular -- the Monster conformal field theory -- is especially ideal, because all of its bulk couplings are irrelevant.
Unification of quantum information theory
NASA Astrophysics Data System (ADS)
Abeyesinghe, Anura
We present the unification of many previously disparate results in noisy quantum Shannon theory and the unification of all of noiseless quantum Shannon theory. More specifically we deal here with bipartite, unidirectional, and memoryless quantum Shannon theory. We find all the optimal protocols and quantify the relationship between the resources used, both for the one-shot and for the ensemble case, for what is arguably the most fundamental task in quantum information theory: sharing entangled states between a sender and a receiver. We find that all of these protocols are derived from our one-shot superdense coding protocol and relate nicely to each other. We then move on to noisy quantum information theory and give a simple, direct proof of the "mother" protocol, or rather her generalization to the Fully Quantum Slepian-Wolf protocol (FQSW). FQSW simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim, and Winter as well as a new class of distributed compression protocols for correlated quantum sources, which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.
Generalized quantum secret sharing
Singh, Sudhir Kumar; Srikanth, R.
2005-01-01
We explore a generalization of quantum secret sharing (QSS) in which classical shares play a complementary role to quantum shares, exploring further consequences of an idea first studied by Nascimento, Mueller-Quade, and Imai [Phys. Rev. A 64, 042311 (2001)]. We examine three ways, termed inflation, compression, and twin thresholding, by which the proportion of classical shares can be augmented. This has the important application that it reduces quantum (information processing) players by replacing them with their classical counterparts, thereby making quantum secret sharing considerably easier and less expensive to implement in a practical setting. In compression, a QSS scheme is turned into an equivalent scheme with fewer quantum players, compensated for by suitable classical shares. In inflation, a QSS scheme is enlarged by adding only classical shares and players. In a twin-threshold scheme, we invoke two separate thresholds for classical and quantum shares based on the idea of information dilution.
Fewster, Christopher J
2015-08-06
The framework of locally covariant quantum field theory is discussed, motivated in part using 'ignorance principles'. It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be expressed via natural isomorphisms between the corresponding functors. The inhomogeneous scalar field is used to illustrate the ideas. It is argued that there are two reasonable definitions of the local physical content associated with a locally covariant theory; when these coincide, the theory is said to be dynamically local. The status of the dynamical locality condition is reviewed, as are its applications in relation to (i) the foundational question of what it means for a theory to represent the same physics in different space-times and (ii) a no-go result on the existence of natural states.
NASA Astrophysics Data System (ADS)
Luna Acosta, German Aurelio
The masses of observed hadrons are fitted according to the kinematic predictions of Conformal Relativity. The hypothesis gives a remarkably good fit. The isospin SU(2) gauge invariant Lagrangian L(,(pi)NN)(x,(lamda)) is used in the calculation of d(sigma)/d(OMEGA) to 2nd-order Feynman graphs for simplified models of (pi)N(--->)(pi)N. The resulting infinite mass sums over the nucleon (Conformal) families are done via the Generalized-Sommerfeld-Watson Transform Theorem. Even though the models are too simple to be realistic, they indicate that if (DELTA)-internal lines were to be included, 2nd-order Feynman graphs may reproduce the experimental data qualitatively. The energy -dependence of the propagator and couplings in Conformal QFT is different from that of ordinary QFT. Suggestions for further work are made in the areas of ultra-violet divergences and OPEC calculations.
Generalized local frame transformation theory for Rydberg atoms in external fields
NASA Astrophysics Data System (ADS)
Giannakeas, Panagiotis; Robicheaux, Francis; Greene, Chris H.
2016-05-01
In this work a rigorous theoretical framework is developed generalizing the local frame transformation theory (GLFT) and it is applied to the photoionization spectra of Rydberg atoms in an external electric field. The resulting development is compared with previous theoretical treatments, including the first version of local frame transformation theory, developed initially by Fano and Harmin. Our revised version of the theory yields non-trivial corrections because we now take into account the full Hilbert space on the energy shell without adopting truncations utilized by the original Fano-Harmin theory. The semi-analytical calculations from GLFT approach are compared with ab initio numerical simulations yielding errors of few tens of MHz whereas the errors in the original Fano-Harmin theory are one or two orders of magnitude larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet modern experimental standards. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award numbers DE-SC0010545 (for PG and CHG) and DE-SC0012193 (for FR).
Basharov, A. M.
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Approximate light cone effects in a nonrelativistic quantum field theory after a local quench
NASA Astrophysics Data System (ADS)
Bertini, Bruno
2017-02-01
We study the spreading of correlations after a local quench in a nonrelativistic quantum field theory. We focus on noninteracting nonrelativistic fermions and study the time evolution after two identical systems in their ground states are suddenly joined together with a localized impurity at the junction. We find that, even if the quasiparticles of the system have unbounded dispersion, the correlations show light cone effects. We carry out a detailed study of these effects by developing an accurate asymptotic expansion of the two-point function and determining exactly the density of particles at any time after the quench. In particular, we find that the width of the light cone region is ∝t1 /2 . The structure of correlations, however, does not show a pure light cone form: "superluminal corrections" are much larger than in the bounded-dispersion case. These findings can be explained by inspecting the structure of excitations generated by the initial state. We show that a similar picture also emerges in the presence of a harmonic trapping potential and when more than two systems are suddenly joined at a single point.
NASA Astrophysics Data System (ADS)
Kushwaha, Manvir S.
2016-03-01
We investigate a one-component, quasi-zero-dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron energy loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in diverse fields such as quantum computing and medical imaging.
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
Quantum Information Theory - an Invitation
NASA Astrophysics Data System (ADS)
Werner, Reinhard F.
Quantum information and quantum computers have received a lot of public attention recently. Quantum computers have been advertised as a kind of warp drive for computing, and indeed the promise of the algorithms of Shor and Grover is to perform computations which are extremely hard or even provably impossible on any merely ``classical'' computer.In this article I shall give an account of the basic concepts of quantum information theory is given, staying as much as possible in the area of general agreement.The article is divided into two parts. The first (up to the end of Sect. 2.5) is mostly in plain English, centered around the exploration of what can or cannot be done with quantum systems as information carriers. The second part, Sect. 2.6, then gives a description of the mathematical structures and of some of the tools needed to develop the theory.
Quantum Electrodynamics: Theory
Lincoln, Don
2016-03-30
The Standard Model of particle physics is composed of several theories that are added together. The most precise component theory is the theory of quantum electrodynamics or QED. In this video, Fermilab’s Dr. Don Lincoln explains how theoretical QED calculations can be done. This video links to other videos, giving the viewer a deep understanding of the process.
Quantum Electrodynamics: Theory
Lincoln, Don
2016-07-12
The Standard Model of particle physics is composed of several theories that are added together. The most precise component theory is the theory of quantum electrodynamics or QED. In this video, Fermilabâs Dr. Don Lincoln explains how theoretical QED calculations can be done. This video links to other videos, giving the viewer a deep understanding of the process.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S.
2006-12-15
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
General covariance from the quantum renormalization group
NASA Astrophysics Data System (ADS)
Shyam, Vasudev
2017-03-01
The quantum renormalization group (QRG) is a realization of holography through a coarse-graining prescription that maps the beta functions of a quantum field theory thought to live on the "boundary" of some space to holographic actions in the "bulk" of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the D +1 dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the D dimensional boundary. This will be a particular form of the Wess-Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Poisson bracket algebra. In particular, it will require the metric beta function to be of the gradient form.
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory.
Gnutzmann, Sven; Waltner, Daniel
2016-03-01
In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.
"Loops and Legs in Quantum Field Theory", 12th DESY Workshop on Elementary Particle Physics
NASA Astrophysics Data System (ADS)
The bi-annual international conference "Loops and Legs in Quantum Field Theory" has been held at Weimar, Germany, from April 27 to May 02, 2014. It has been the 12th conference of this series, started in 1992. The main focus of the conference are precision calculations of multi- loop and multi-leg processes in elementary particle physics for processes at present and future high-energy facilities within and beyond the Standard Model. At present many physics questions studied deal with processes at the LHC and future facilities like the ILC. A growing number of contributions deals with important developments in the field of computational technologies and algorithmic methods, including large-scale computer algebra, efficient methods to compute large numbers of Feynman diagrams, analytic summation and integration methods of various kinds, new related function spaces, precise numerical methods and Monte Carlo simulations. The present conference has been attended by more than 110 participants from all over the world, presenting more than 75 contributions, most of which have been written up for these pro- ceedings. The present volume demonstrates in an impressive way the enormous development of the field during the last few years, reaching the level of 5-loop calculations in QCD and a like- wise impressive development in massive next-to-leading order and next-to-next-to-leading order processes. Computer algebraic and numerical calculations require terabyte storage and many CPU years, even after intense parallelization, to obtain state-of-the-art theoretical predictions. The city of Weimar gave a suitable frame to the conference, with its rich history, especially in literature, music, arts, and architecture. Goethe, Schiller, Wieland, Herder, Bach and Liszt lived there and created many of their masterpieces. The many young participants signal that our field is prosperous and faces an exciting future. The conference hotel "Kaiserin Augusta" offered a warm hospitality and
Relativistic Two and Three-Particle Bound States in Scalar Quantum Field Theory.
NASA Astrophysics Data System (ADS)
di Leo, Leo
This thesis is concerned with the application of the variational method, within the Hamiltonian formalism of quantum field theory (QFT), to describe relativistic two and three particle states in scalar field theories. Two models are considered: scalar particles interacting through the exchange of scalar quanta, and the Higgs sector of the Minimal Standard Model. We derive relativistic particle-antiparticle wave equations for scalar particles, phi and |phi, interacting via a massive or massless scalar field, chi (the Wick-Cutkosky model), using simple Fock space ansatze. The variational method, within the Hamiltonian formalism of QFT, is used to derive equations with and without coupling of this quasi-bound phi|phi system to the chichi decay channel. The equations are then approximately decoupled to yield a relativistic momentum-space (Schrodinger-like) wave equation from which we determine bound-state energies numerically, perturbatively or variationally for various strengths of the coupling. Bound-state energies in the massless case are compared to the known ladder Bethe-Salpeter and light-cone solutions of this model. In the case of coupling to the decay channel, which is easily accomplished in the present formalism by expanding our Fock-space ansatz, the quasi-bound phi|phi states are seen to arise as resonances in the chichi scattering cross section. Numerical results are presented for the massive and massless chi case for various coupling strengths. The same variational method can be easily extended to derive relativistic three-particle wave equations for scalar particles phi,phi and |phi, interacting via a massive or massless scalar field, chi. In this case, the equations are obtained using a simple |phiphi|phi > +| phiphi|{phi}chi > ansatz. Approximate variational solutions (using product-type hydrogenic wave functions) of these equations are presented for various strengths of the coupling. The magnitude of the relativistic effects in the three
Tscherbul, T V; Dalgarno, A
2010-11-14
An efficient method is presented for rigorous quantum calculations of atom-molecule and molecule-molecule collisions in a magnetic field. The method is based on the expansion of the wave function of the collision complex in basis functions with well-defined total angular momentum in the body-fixed coordinate frame. We outline the general theory of the method for collisions of diatomic molecules in the (2)Σ and (3)Σ electronic states with structureless atoms and with unlike (2)Σ and (3)Σ molecules. The cross sections for elastic scattering and Zeeman relaxation in low-temperature collisions of CaH((2)Σ(+)) and NH((3)Σ(-)) molecules with (3)He atoms converge quickly with respect to the number of total angular momentum states included in the basis set, leading to a dramatic (>10-fold) enhancement in computational efficiency compared to the previously used methods [A. Volpi and J. L. Bohn, Phys. Rev. A 65, 052712 (2002); R. V. Krems and A. Dalgarno, J. Chem. Phys. 120, 2296 (2004)]. Our approach is thus well suited for theoretical studies of strongly anisotropic molecular collisions in the presence of external electromagnetic fields.
Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
NASA Astrophysics Data System (ADS)
Braathen, Johannes; Goodsell, Mark D.
2016-12-01
We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an "on-shell" condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions — opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.
BOOK REVIEW: Modern Canonical Quantum General Relativity
NASA Astrophysics Data System (ADS)
Kiefer, Claus
2008-06-01
The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly divided into two classes: either one seeks a unified quantum framework of all interactions or one starts with a direct quantization of general relativity. In the first class, string theory (M-theory) is the only known example. In the second class, one can make an additional methodological distinction: while covariant approaches such as path-integral quantization use the four-dimensional metric as an essential ingredient of their formalism, canonical approaches start with a foliation of spacetime into spacelike hypersurfaces in order to arrive at a Hamiltonian formulation. The present book is devoted to one of the canonical approaches—loop quantum gravity. It is named modern canonical quantum general relativity by the author because it uses connections and holonomies as central variables, which are analogous to the variables used in Yang Mills theories. In fact, the canonically conjugate variables are a holonomy of a connection and the flux of a non-Abelian electric field. This has to be contrasted with the older geometrodynamical approach in which the metric of three-dimensional space and the second fundamental form are the fundamental entities, an approach which is still actively being pursued. It is the author's ambition to present loop quantum gravity in a way in which every step is formulated in a mathematically rigorous form. In his own words: 'loop quantum gravity is an attempt to construct a mathematically rigorous, background-independent, non-perturbative quantum field theory of Lorentzian general relativity and all known matter in four spacetime dimensions, not more and not less'. The formal Leitmotiv of loop quantum gravity is background independence. Non-gravitational theories are usually quantized on a given non-dynamical background. In contrast, due to
NASA Astrophysics Data System (ADS)
Trojnar, Anna H.; Kadantsev, Eugene S.; Korkusiński, Marek; Hawrylak, Pawel
2011-12-01
A theory of the fine structure of correlated exciton states in self-assembled parabolic semiconductor quantum dots in a magnetic field perpendicular to the quantum dot plane is presented. The correlated exciton wave function is expanded in configurations consisting of products of electron and heavy-hole 2D harmonic oscillator states (HO) in a magnetic field and the electron spin Sz=±1/2 and a heavy-hole spin τz=±3/2 states. Analytical expressions for the short- and long-range electron-hole exchange Coulomb interaction matrix elements are derived in the HO and spin basis for arbitrary magnetic field. This allows the incorporation of short- and long-range electron-hole exchange, direct electron-hole interaction, and quantum dot anisotropy in the exact diagonalization of the exciton Hamiltonian. The fine structure of ground and excited correlated exciton states as a function of a number of confined shells, quantum dot anisotropy, and magnetic field is obtained using exact diagonalization of the many-body Hamiltonian. The effects of correlations are shown to significantly affect the energy splitting of the two bright exciton states.
NASA Astrophysics Data System (ADS)
Zeh, H. D.
1999-04-01
This is a brief reply to S. Goldstein's article "Quantum theory without observers" in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Exact quantum field mappings between different experiments on quantum gases
NASA Astrophysics Data System (ADS)
Wamba, Etienne; Pelster, Axel; Anglin, James R.
2016-10-01
Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or nonequilibrium states prevent exact solutions. Here we present a different kind of exact result, which applies even in the absence of actual solutions: a class of space-time mappings of different experiments onto each other. Since our result is an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics, it is extremely general; it applies to arbitrary measurements on any mixtures of Bose or Fermi gases, in arbitrary initial states. It represents a strong prediction of quantum field theory which can be tested in current laboratories, and whose practical applications include perfect simulation of interesting experiments with other experiments which may be easier to perform.
Gao, Yi; Neuhauser, Daniel
2012-08-21
We develop an approach for dynamical (ω > 0) embedding of mixed quantum mechanical (QM)/classical (or more precisely QM/electrodynamics) systems with a quantum sub-region, described by time-dependent density functional theory (TDDFT), within a classical sub-region, modeled here by the recently proposed near-field (NF) method. Both sub-systems are propagated simultaneously and are coupled through a common Coulomb potential. As a first step we implement the method to study the plasmonic response of a metal film which is half jellium-like QM and half classical. The resulting response is in good agreement with both full-scale TDDFT and the purely classical NF method. The embedding method is able to describe the optical response of the whole system while capturing quantum mechanical effects, so it is a promising approach for studying electrodynamics in hybrid molecules-metals nanostructures.
Generalized mean-field theory for Ising spins in small world networks.
Meilikhov, E Z; Farzetdinova, R M
2005-04-01
A generalization of mean-field theory for random systems is described. The results of that analytic model could be reconciled with the results of numerical calculations of the Curie temperature for a system of Ising spins in small world (SW) networks by introducing the effective interaction energy associated with long-range links which exceeds the real energy of spin interaction. Such a model describes qualitatively well the increasing Curie temperature T(C) with the growth of the long-range links fraction p in the two-dimensional SW system with fixed coordination number. On the basis of simple physical considerations, concentration dependences T(C)(p) are found for SW systems of different dimensions.
Recoverability in quantum information theory
NASA Astrophysics Data System (ADS)
Wilde, Mark
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.
General properties of quantum optical systems in a strong field limit
NASA Technical Reports Server (NTRS)
Chumakov, S. M.; Klimov, Andrei B.
1994-01-01
We investigate the dynamics of an arbitrary atomic system (n-level atoms or many n-level atoms) interacting with a resonant quantized mode of an em field. If the initial field state is a coherent state with a large photon number then the system dynamics possesses some general features, independently of the particular structure of the atomic system. Namely, trapping states, factorization of the wave function, collapses and revivals of the atomic energy oscillations are discussed.
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
NASA Astrophysics Data System (ADS)
Bonora, L.; Bytsenko, A. A.; Gonçalves, A. E.
2016-11-01
We derive formulas for the classical Chern-Simons invariant of irreducible SU( n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Mariño-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.
Generalized mutual information of quantum critical chains
NASA Astrophysics Data System (ADS)
Alcaraz, F. C.; Rajabpour, M. A.
2015-04-01
We study the generalized mutual information I˜n of the ground state of different critical quantum chains. The generalized mutual information definition that we use is based on the well established concept of the Rényi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete Z (Q ) symmetries (Q -state Potts model with Q =2 ,3 ,4 and Z (Q ) parafermionic models with Q =5 ,6 ,7 ,8 and also Ashkin-Teller model with different anisotropies) or the U (1 ) continuous symmetries (Klein-Gordon field theory, X X Z and spin-1 Fateev-Zamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the ground-state wave functions in two special bases. Our results indicate some general behavior for particular ranges of values of the parameter n that defines I˜n. For a system, with total size L and subsystem sizes ℓ and L -ℓ , the I˜n has a logarithmic leading behavior given by c/˜n4 log[L/π sin(π/ℓ L ) ] where the coefficient c˜n is linearly dependent on the central charge c of the underlying conformal field theory describing the system's critical properties.
Magnetic field effects in few-level quantum dots: Theory and application to experiment
NASA Astrophysics Data System (ADS)
Wright, Christopher J.; Galpin, Martin R.; Logan, David E.
2011-09-01
We examine several effects of an applied magnetic field on Anderson-type models for both single- and two-level quantum dots, and we make direct comparison between numerical renormalization group (NRG) calculations and recent conductance measurements. On the theoretical side, the focus is on magnetization, single-particle dynamics, and zero-bias conductance, with emphasis on the universality arising in strongly correlated regimes, including a method to obtain the scaling behavior of field-induced Kondo resonance shifts over a very wide field range. NRG is also used to interpret recent experiments on spin-(1)/(2) and spin-1 quantum dots in a magnetic field, which we argue do not wholly probe universal regimes of behavior, and the calculations are shown to yield good qualitative agreement with essentially all features seen in experiment. The results capture in particular the observed field dependence of the Kondo conductance peak in a spin-(1)/(2) dot, with quantitative deviations from experiment occurring at fields in excess of ˜5T, indicating the eventual inadequacy of using the equilibrium single-particle spectrum to calculate the conductance at finite bias.
Basics of quantum field theory of electromagnetic interaction processes in single-layer graphene
NASA Astrophysics Data System (ADS)
Hieu Nguyen, Van
2016-09-01
The content of this work is the study of electromagnetic interaction in single-layer graphene by means of the perturbation theory. The interaction of electromagnetic field with Dirac fermions in single-layer graphene has a peculiarity: Dirac fermions in graphene interact not only with the electromagnetic wave propagating within the graphene sheet, but also with electromagnetic field propagating from a location outside the graphene sheet and illuminating this sheet. The interaction Hamiltonian of the system comprising electromagnetic field and Dirac fermions fields contains the limits at graphene plane of electromagnetic field vector and scalar potentials which can be shortly called boundary electromagnetic field. The study of S-matrix requires knowing the limits at graphene plane of 2-point Green functions of electromagnetic field which also can be shortly called boundary 2-point Green functions of electromagnetic field. As the first example of the application of perturbation theory, the second order terms in the perturbative expansions of boundary 2-point Green functions of electromagnetic field as well as of 2-point Green functions of Dirac fermion fields are explicitly derived. Further extension of the application of perturbation theory is also discussed.
Schumaker, B.L.
1985-01-01
This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum-mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and momentum variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes arise from two-proton transitions, i.e., are created or destroyed two at a time. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed. The fifth paper considers the validity of the standard quantum limit (SQL) for measurements that monitor the position of a free mass. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models and of the gravitational waves they emit.
Beyond generalized Proca theories
NASA Astrophysics Data System (ADS)
Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji
2016-09-01
We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.
Electric fields and quantum wormholes
NASA Astrophysics Data System (ADS)
Engelhardt, Dalit; Freivogel, Ben; Iqbal, Nabil
2015-09-01
Electric fields can thread a classical Einstein-Rosen bridge. Maldacena and Susskind have recently suggested that in a theory of dynamical gravity the entanglement of ordinary perturbative quanta should be viewed as creating a quantum version of an Einstein-Rosen bridge between the particles, or a "quantum wormhole." We demonstrate within low-energy effective field theory that there is a precise sense in which electric fields can also thread such quantum wormholes. We define a nonperturbative "wormhole susceptibility" that measures the ease of passing an electric field through any sort of wormhole. The susceptibility of a quantum wormhole is suppressed by powers of the U (1 ) gauge coupling relative to that for a classical wormhole but can be made numerically equal with a sufficiently large amount of entangled matter.
Wieser, R
2017-05-04
A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S = 1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.
NASA Astrophysics Data System (ADS)
Salam, Abdus; Wigner, E. P.
2010-03-01
Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.
Holomorphic field realization of SH c and quantum geometry of quiver gauge theories
NASA Astrophysics Data System (ADS)
Bourgine, Jean-Emile; Matsuo, Yutaka; Zhang, Hong
2016-04-01
In the context of 4D/2D dualities, SH c algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of N=2 supersymmetricgaugetheories. Inthispaper,werewritetheSH c algebrainterms of three holomorphic fields D 0( z), D ±1( z) with which the algebra and its representations are simplified. The instanton partition functions for arbitrary N=2 super Yang-Mills theories with A n and A n (1) type quiver diagrams are compactly expressed as a product of four building blocks, Gaiotto state, dilatation, flavor vertex operator and intertwiner which are written in terms of SH c and the orthogonal basis introduced by Alba, Fateev, Litvinov and Tarnopolskiy. These building blocks are characterized by new conditions which generalize the known ones on the Gaiotto state and the Carlsson-Okounkov vertex. Consistency conditions of the inner product give algebraic relations for the chiral ring generating functions defined by Nekrasov, Pestun and Shatashvili. In particular we show the polynomiality of the qq-characters which have been introduced as a deformation of the Yangian characters. These relations define a second quantization of the Seiberg-Witten geometry, and, accordingly, reduce to a Baxter TQ-equation in the Nekrasov-Shatashvili limit of the Omega-background.
Control of noisy quantum systems: Field-theory approach to error mitigation
NASA Astrophysics Data System (ADS)
Hipolito, Rafael; Goldbart, Paul M.
2016-04-01
We consider the basic quantum-control task of obtaining a target unitary operation (i.e., a quantum gate) via control fields that couple to the quantum system and are chosen to best mitigate errors resulting from time-dependent noise, which frustrate this task. We allow for two sources of noise: fluctuations in the control fields and fluctuations arising from the environment. We address the issue of control-error mitigation by means of a formulation rooted in the Martin-Siggia-Rose (MSR) approach to noisy, classical statistical-mechanical systems. To do this, we express the noisy control problem in terms of a path integral, and integrate out the noise to arrive at an effective, noise-free description. We characterize the degree of success in error mitigation via a fidelity metric, which characterizes the proximity of the sought-after evolution to ones that are achievable in the presence of noise. Error mitigation is then best accomplished by applying the optimal control fields, i.e., those that maximize the fidelity subject to any constraints obeyed by the control fields. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh (SK) path integral, with the added twist that the "forward" and "backward" branches of the time contour are inequivalent with respect to the noise. The present approach naturally and readily allows the incorporation of constraints on the control fields—a useful feature in practice, given that constraints feature in all real experiments. In addition to addressing the noise average of the fidelity, we consider its full probability distribution. The information content present in this distribution allows one to address more complex questions regarding error mitigation, including, in principle, questions of extreme value statistics, i.e., the likelihood and impact of rare instances of the fidelity and how to harness or cope with their influence. We illustrate this MSR-SK reformulation by considering a model
Quantum cellular automaton theory of light
Bisio, Alessandro D’Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-15
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space–time and mechanics (D’Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Quantum cellular automaton theory of light
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-01
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space-time and mechanics (D'Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Quantum theory of Thomson scattering
NASA Astrophysics Data System (ADS)
Crowley, B. J. B.; Gregori, G.
2014-12-01
The general theory of the scattering of electromagnetic radiation in atomic plasmas and metals, in the non-relativistic regime, in which account is taken of the Kramers-Heisenberg polarization terms in the Hamiltonian, is described from a quantum mechanical viewpoint. As well as deriving the general formula for the double differential Thomson scattering cross section in an isotropic finite temperature multi-component system, this work also considers closely related phenomena such as absorption, refraction, Raman scattering, resonant (Rayleigh) scattering and Bragg scattering, and derives many essential relationships between these quantities. In particular, the work introduces the concept of scattering strength and the strength-density field which replaces the normal particle density field in the standard treatment of scattering by a collection of similar particles and it is the decomposition of the strength-density correlation function into more familiar-looking components that leads to the final result. Comparisons are made with previous work, in particular that of Chihara [1].
Chen Zhangjin; Lin, C. D.; Liang Yaqiu
2010-06-25
Based on the full quantal recollision model and field-free electron impact ionization theory, we calculate the correlated momentum spectra of the two outgoing electrons in strong field nonsequential double ionization (NSDI) of helium to compare with recent experiments. By analyzing the relative strength of binary versus recoil collisions exhibited in the photoelectron spectra, we confirm that the observed fingerlike structure in the experiment is a consequence of the Coulomb interaction between the two emitted electrons. Our result supports the recollision mechanism of strong field NSDI at the most fundamental level.
Chen, Zhangjin; Liang, Yaqiu; Lin, C D
2010-06-25
Based on the full quantal recollision model and field-free electron impact ionization theory, we calculate the correlated momentum spectra of the two outgoing electrons in strong field nonsequential double ionization (NSDI) of helium to compare with recent experiments. By analyzing the relative strength of binary versus recoil collisions exhibited in the photoelectron spectra, we confirm that the observed fingerlike structure in the experiment is a consequence of the Coulomb interaction between the two emitted electrons. Our result supports the recollision mechanism of strong field NSDI at the most fundamental level.
An Introduction to Effective Field Theory
NASA Astrophysics Data System (ADS)
Burgess, C. P.
2007-11-01
This review summarizes effective field theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described and evaluated explicitly for a simple model. Power-counting results are illustrated for a few cases of practical interest, and several applications to quantum electrodynamics are described.
A nilpotent symmetry of quantum gauge theories
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment
DOE R&D Accomplishments Database
Marcus, R. A.
1964-01-01
In its usual form activated complex theory assumes a quasi-equilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced.
NASA Astrophysics Data System (ADS)
Höhn, Philipp Andres; Wever, Christopher S. P.
2017-01-01
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S 's state as O 's "catalog of knowledge" about S . From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C2N; (b) states evolve unitarily under the group PSU (2N) according to the von Neumann evolution equation; and (c) O 's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels previously unnoticed structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a "charge of quantum theory" and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in a companion paper (P. Höhn, arXiv:1412.8323).
On supersymmetric Lifshitz field theories
NASA Astrophysics Data System (ADS)
Chapman, Shira; Oz, Yaron; Raviv-Moshe, Avia
2015-10-01
We consider field theories that exhibit a supersymmetric Lifshitz scaling with two real supercharges. The theories can be formulated in the language of stochastic quan-tization. We construct the free field supersymmetry algebra with rotation singlet fermions for an even dynamical exponent z = 2 k in an arbitrary dimension. We analyze the classical and quantum z = 2 supersymmetric interactions in 2 + 1 and 3 + 1 spacetime dimensions and reveal a supersymmetry preserving quantum diagrammatic cancellation. Stochastic quantization indicates that Lifshitz scale invariance is broken in the (3 + 1)-dimensional quantum theory.
Quantum Transition State Theory
NASA Astrophysics Data System (ADS)
Waalkens, Holger
2009-03-01
The main idea of Wigner's transition state theory (TST) is to compute reaction rates from the flux through a dividing surface placed between reactants and products. In order not to overestimate the rate the dividing surface needs to have the no- recrossing property, i.e. reactive trajectories cross the dividing surface exactly once, and nonreactive trajectories do not cross it at all. The long standing problem of how to construct such a diving surface for multi-degree-of-freedom systems was solved only recently using ideas from dynamical systems theory. Here a normal form allows for a local decoupling of the classical dynamics which leads to the explicit construction of the phase space structures that govern the reaction dynamics through transition states. The dividing surface is spanned by a normally hyperbolic manifold which is the mathematical manifestation of the transition state as an unstable invariant subsystem of one degree of freedom less than the full system. The mere existence of a quantum version of TST is discussed controversially in the literature. The key isssue is the presence of quantum mechanical tunneling which prohibits the existence of a local theory analogous to the classical case. Various approaches have been devloped to overcome this problem by propagating quantum wavefunctions through the transition state region. These approaches have in common that they are computationally very expensive which seriously limits their applicability. In contrast the approach by Roman Schubert, Stephen Wiggins and myself is local in nature. A quantum normal form allows us to locally decouple the quantum dynamics to any desired order in Planck's constant. This yields not only the location of the scattering and resonance wavefunctions relative to the classical phase space structures, but also leads to very efficient algorithms to compute cumulative reaction probabilities and Gamov-Siegert resonances which are the quantum imprints of the transition state.
NASA Astrophysics Data System (ADS)
Habegger, Eric John
2005-02-01
It is theorized that the quantum vacuum is a random electromagnetic field that permeates the universe. It will be shown that acceleration between a quark and a random electromagnetic energy field is an analog of the reaction between a charge moving at constant velocity with respect to an organized electromagnetic field. The difference is that with a quark any natural perpendicular deflection during that motion, as predicted by Lorentz, is contained by the strong force, which results in a change in the angular momentum of the spin of a quark. The first derivative of the equations of motion of charges in an organized electromagnetic field may be used when applied to a random electromagnetic field to invoke the same fields modeled by Maxwell's equations. Mass is intimately bound up with a quark's spin angular momentum and the energy for that increase comes directly from the local field. The underlying randomness of the local field normally remains intact through these energy exchanges but it is speculated that in a quantum entanglement, an absolute level of order is imposed on the field along a path between two particles. This causes the non local effects seen in quantum entanglement. The mechanism that may cause this effect is discussed and a simple experiment is proposed that can test the hypothesis. Also discussed are new theoretical constructs for electromagnetic radiation, mass, the skin effect, self-inductance, superposition, and gravity. The emphasis will be on an intuitive and logical approach more than a mathematical approach.
Revisiting Bohr's semiclassical quantum theory.
Ben-Amotz, Dor
2006-10-12
Bohr's atomic theory is widely viewed as remarkable, both for its accuracy in predicting the observed optical transitions of one-electron atoms and for its failure to fully correspond with current electronic structure theory. What is not generally appreciated is that Bohr's original semiclassical conception differed significantly from the Bohr-Sommerfeld theory and offers an alternative semiclassical approximation scheme with remarkable attributes. More specifically, Bohr's original method did not impose action quantization constraints but rather obtained these as predictions by simply matching photon and classical orbital frequencies. In other words, the hydrogen atom was treated entirely classically and orbital quantized emerged directly from the Planck-Einstein photon quantization condition, E = h nu. Here, we revisit this early history of quantum theory and demonstrate the application of Bohr's original strategy to the three quintessential quantum systems: an electron in a box, an electron in a ring, and a dipolar harmonic oscillator. The usual energy-level spectra, and optical selection rules, emerge by solving an algebraic (quadratic) equation, rather than a Bohr-Sommerfeld integral (or Schroedinger) equation. However, the new predictions include a frozen (zero-kinetic-energy) state which in some (but not all) cases lies below the usual zero-point energy. In addition to raising provocative questions concerning the origin of quantum-chemical phenomena, the results may prove to be of pedagogical value in introducing students to quantum mechanics.
Three-Dimensional Topological Field Theory Induced from Generalized Complex Structure
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki
We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold X to an arbitrary generalized complex manifold M. The theory is invariant under the diffeomorphism on the worldvolume and the b-transformation on the generalized complex structure. Moreover the model is manifestly invariant under the mirror symmetry. We derive from this model the Zucchini's two-dimensional topological sigma model with a generalized complex structure as a boundary action on ∂X. As a special case, we obtain three-dimensional realization of a WZ-Poisson manifold.
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
complicated non-rational theories. Examples include critical percolation, supersymmetric string backgrounds, disordered electronic systems, sandpile models describing avalanche processes, and so on. In each case, the non-rationality and non-unitarity of the CFT suggested that a more general theoretical framework was needed. Driven by the desire to better understand these applications, the mid-1990s saw significant theoretical advances aiming to generalise the constructs of rational CFT to a more general class. In 1994, Nahm introduced an algorithm for computing the fusion product of representations which was significantly generalised two years later by Gaberdiel and Kausch who applied it to explicitly construct (chiral) representations upon which the energy operator acts non-diagonalisably. Their work made it clear that underlying the physically relevant correlation functions are classes of reducible but indecomposable representations that can be investigated mathematically to the benefit of applications. In another direction, Flohr had meanwhile initiated the study of modular properties of the characters of logarithmic CFTs, a topic which had already evoked much mathematical interest in the rational case. Since these seminal theoretical papers appeared, the field has undergone rapid development, both theoretically and with regard to applications. Logarithmic CFTs are now known to describe non-local observables in the scaling limit of critical lattice models, for example percolation and polymers, and are an integral part of our understanding of quantum strings propagating on supermanifolds. They are also believed to arise as duals of three-dimensional chiral gravity models, fill out hidden sectors in non-rational theories with non-compact target spaces, and describe certain transitions in various incarnations of the quantum Hall effect. Other physical applications range from two-dimensional turbulence and non-equilibrium systems to aspects of the AdS/CFT correspondence and
Quantum thermodynamics of general quantum processes.
Binder, Felix; Vinjanampathy, Sai; Modi, Kavan; Goold, John
2015-03-01
Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorizes the output state. Moreover, the change in entropy is also positive for the same majorization condition. This makes a strong connection between the two operational laws of thermodynamics.
NASA Astrophysics Data System (ADS)
Dunne, Gerald V.; Ünsal, Mithat
2016-10-01
We present a broad conceptual introduction to some new ideas in nonperturbative quantum field theory (QFT) that have led to progress toward an understanding of quark confinement in gauge theories and, more broadly, toward a nonperturbative continuum definition of QFTs. We first present exact orbifold equivalences of supersymmetric and nonsupersymmetric QFTs in the large-N limit and exact equivalences of large-N theories in infinite volume to large-N theories in finite volume, or even at a single point. We discuss principles by which calculable QFTs are continuously connected to strong-coupling QFTs, allowing understanding of the physics of confinement or the absence thereof. We discuss the role of particular saddle solutions, termed bions, in weak-coupling calculable regimes. The properties of bions motivate an extension of semiclassical methods used to evaluate functional integrals to include families of complex saddles (Picard-Lefschetz theory). This analysis leads us to the resurgence program, which may provide a framework for combining divergent perturbation series with semiclassical instanton and bion/renormalon contributions. This program could provide a nonperturbative definition of the path integral.
Strong-field effects and time asymmetry in general relativity and in bimetric gravitation theory
NASA Astrophysics Data System (ADS)
Damour, Thibault
1984-10-01
The concepts underlying our present theoretical understanding of the radiative two-condensed-body problem in general relativity and in bimetric gravitation theory are critically reviewed. The relevance of the 1935 Einstein-Rosen “bridge” article is emphasized. The possibility (first suggested by N. Rosen, for the linearized approximation) of extending to gravity the Wheeler-Feynman time-symmetric approach is questioned.
Lu, N.; Zhu, S. )
1989-11-15
A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL's) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering {ital Q} function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL's analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state {ital Q} functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.
Remote State Preparation for Quantum Fields
NASA Astrophysics Data System (ADS)
Ber, Ran; Zohar, Erez
2016-07-01
Remote state preparation is generation of a desired state by a remote observer. In spite of causality, it is well known, according to the Reeh-Schlieder theorem, that it is possible for relativistic quantum field theories, and a "physical" process achieving this task, involving superoscillatory functions, has recently been introduced. In this work we deal with non-relativistic fields, and show that remote state preparation is also possible for them, hence obtaining a Reeh-Schlieder-like result for general fields. Interestingly, in the nonrelativistic case, the process may rely on completely different resources than the ones used in the relativistic case.
Gauge theories under incorporation of a generalized uncertainty principle
Kober, Martin
2010-10-15
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Non-perturbative effects in quantum field theory: QCD, supersymmetric QCD and axions
NASA Astrophysics Data System (ADS)
Wu, Weitao
In the study of non-perturbative effects in four dimenstional non-Abelian gauge theories, instantons have played an important conceptual role. However, their role in the quantitative understanding these theories has remained obscure. In the first part of this thesis, we revisit the question of whether or not one can perform reliable semiclassical QCD computation at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of semiclassical calculation. For N f > Nc, a systematic computation is possible; for Nf < Nc, it is not. Nf = Nc is a borderline case. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit. Supersymmetry has provided a tool with which to obtain a range of exact results in field theory and string theory. Arguably the first inkling that one could obtain such results was the work of Novikov, Shifman, Vainshtein, and Zakharov (NSVZ). They argued for two exact results in gauge theories using instanton computation. First, that one could compute certain correlation functions exactly at weak coupling, and extend the results to strong coupling; second, that one could obtain exact expressions for beta-functions. However, each of these results raised questions. As methods exploiting systematic weak coupling expansions and holomorphy were developed, it became clear that the strong coupling instanton computation was incorrect. This in turn called the exact beta-function into question. In the second part of this thesis, we will provide resolutions to both of these questions. First, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. For the question of the NSVZbeta
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Quantum probability from decision theory?
NASA Astrophysics Data System (ADS)
Barnum, H.; Caves, C. M.; Finkelstein, J.; Fuchs, C. A.; Schack, R.
2000-05-01
In a recent paper (quant-ph/9906015), Deutsch claims to derive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." We show that his derivation fails because it includes hidden probabilistic assumptions.
Generalized quantum gravity condensates for homogeneous geometries and cosmology
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Pranzetti, Daniele; Ryan, James P.; Sindoni, Lorenzo
2015-12-01
We construct a generalized class of quantum gravity condensate states that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction also lends itself easily to application to the case of spherically symmetric quantum geometries.
Basic Aspects of the Quantum Theory of Solids
NASA Astrophysics Data System (ADS)
Khomskii, Daniel I.
2010-09-01
1. Some basic notions of the classical and quantum statistical physics; 2. General theory of phase transitions; 3. Bose- and Fermi-statistics; 4. Phonons in crystals; 5. General Bose-systems: Bose-condensation; 6. Magnetism; 7. Electrons in metals; 8. Interacting electrons: Green functions and Feynman diagrams (methods of the field theory in many-particle physics); 9. Electrons with Coulomb interaction; 10. Fermi-liquid theory and its possible generalizations; 11. Instabilities and phase transitions in electronic systems; 12. Strongly correlated electrons; 13. Magnetic impurities in metals, Kondo effect, heavy fermions and mixed valence; References; Index.
NASA Astrophysics Data System (ADS)
Connes, Alain; Kreimer, Dirk
This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop
NASA Astrophysics Data System (ADS)
Nikolopoulos, L. A. A.; Bachau, H.
2016-11-01
In this work we present an ab initio nonperturbative theory for the description of the two-electron dynamics of a spherical quantum dot (QD) in THz and mid-IR ultrashort laser fields. We have approximated the QD's confinement potential to have a Gaussian-like spatial dependence and have calculated its electronic structure and photoionization one-electron cross sections with an ab initio configuration-interaction approach. We have also calculated the ionization yields following the interaction with a laser pulse by numerically solving the time-dependent Schrödinger equation. All results show a strong dependence on the dot size. We have also identified resonances, of the Fano-type, in the photoionization spectrum with properties varying along with the QD size.
A supersymmetric extension of quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2003-01-01
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Orientable Objects in Relativistic Quantum Theory
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Shelepin, A. L.
2017-03-01
An approach to the quantum description of the orientation of relativistic particles, generalizing the approach to nonrelativistic objects possessing orientation (in particular, a rotator) is proposed, based on the self-consistent use of two reference frames. The realization of such an approach is connected with the introduction of wave functions f (x, z) on the Poincaré group M(3,1), which depend on the coordinates x μ of the Minkowski space M(3,1)/Spin(3,1) and orientational variables assigned by the elements z {β/α} of the matrix Z ∈Spin(3,1).The field f (x, z) is the generating function for ordinary spin-tensor fields and admits a number of symmetries. Besides the Lorentz transformations (corresponding to the action of the Poincaré group from the left and interpretable as external symmetries), transformations of a reference frame associated with an orientable object (corresponding to the action of the Poincaré group from the right and interpretable as internal symmetries) are applicable to orientable objects. In addition to the six quantum numbers assigned by the Casimir operators and the left generators, quantum numbers arise here that are assigned by the right generators and are associated with internal symmetries. The assumption that the internal symmetries of the theory of orientable objects are local leads to gauge theories describing the electroweak and gravitational interactions.
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong; Ma, Yongge
2011-09-01
As modified gravity theories, the four-dimensional metric f(R) theories are cast into connection-dynamical formalism with real su(2) connections as configuration variables. This formalism enables us to extend the nonperturbative loop quantization scheme of general relativity to any metric f(R) theories. The quantum kinematical framework of f(R) gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for f(R) theories are well defined. Our results show that the nonperturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
Classical simulation of quantum fields I
NASA Astrophysics Data System (ADS)
Hirayama, T.; Holdom, B.
2006-10-01
We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler-Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In lambda phi(4) theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously.
NASA Astrophysics Data System (ADS)
Othman, Mohamed I. A.; Elmaklizi, Yassmin D.; Said, Samia M.
2013-03-01
The problem of the generalized thermoelastic medium for three different theories under the effect of a gravity field is investigated. The Lord-Shulman (L-S), Green-Lindsay (G-L), and classical-coupled (CD) theories are discussed. The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions for the displacement components, temperature, and stress components are obtained by using normal mode analysis. Numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of gravity. A comparison also is made between the three theories for the results with and without a temperature dependence.
Generalized Geometric Quantum Speed Limits
NASA Astrophysics Data System (ADS)
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Quantum theory of electroabsorption in semiconductor nanocrystals.
Tepliakov, Nikita V; Leonov, Mikhail Yu; Baranov, Alexander V; Fedorov, Anatoly V; Rukhlenko, Ivan D
2016-01-25
We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.
Kirrander, Adam; Shalashilin, Dmitrii V.
2011-09-15
We present an alternate version of the coupled-coherent-state method, specifically adapted for solving the time-dependent Schroedinger equation for multielectron dynamics in atoms and molecules. This theory takes explicit account of the exchange symmetry of fermion particles, and it uses fermion molecular dynamics to propagate trajectories. As a demonstration, calculations in the He atom are performed using the full Hamiltonian and accurate experimental parameters. Single- and double-ionization yields by 160-fs and 780-nm laser pulses are calculated as a function of field intensity in the range 10{sup 14}-10{sup 16} W/cm{sup 2}, and good agreement with experiments by Walker et al. is obtained. Since this method is trajectory based, mechanistic analysis of the dynamics is straightforward. We also calculate semiclassical momentum distributions for double ionization following 25-fs and 795-nm pulses at 1.5x10{sup 15} W/cm{sup 2}, in order to compare them with the detailed experiments by Rudenko et al. For this more challenging task, full convergence is not achieved. However, major effects such as the fingerlike structures in the momentum distribution are reproduced.
Generalized Brans-Dicke theories
De Felice, Antonio; Tsujikawa, Shinji E-mail: shinji@rs.kagu.tus.ac.jp
2010-07-01
In Brans-Dicke theory a non-linear self interaction of a scalar field φ allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and instabilities. A peculiar evolution of the field propagation speed allows us to distinguish those theories from the ΛCDM model.
A coarse-grained generalized second law for holographic conformal field theories
NASA Astrophysics Data System (ADS)
Bunting, William; Fu, Zicao; Marolf, Donald
2016-03-01
We consider the universal sector of a d\\gt 2 dimensional large-N strongly interacting holographic CFT on a black hole spacetime background B. When our CFT d is coupled to dynamical Einstein-Hilbert gravity with Newton constant G d , the combined system can be shown to satisfy a version of the thermodynamic generalized second law (GSL) at leading order in G d . The quantity {S}{CFT}+\\frac{A({H}B,{perturbed})}{4{G}d} is non-decreasing, where A({H}B,{perturbed}) is the (time-dependent) area of the new event horizon in the coupled theory. Our S CFT is the notion of (coarse-grained) CFT entropy outside the black hole given by causal holographic information—a quantity in turn defined in the AdS{}d+1 dual by the renormalized area {A}{ren}({H}{{bulk}}) of a corresponding bulk causal horizon. A corollary is that the fine-grained GSL must hold for finite processes taken as a whole, though local decreases of the fine-grained generalized entropy are not obviously forbidden. Another corollary, given by setting {G}d=0, states that no finite process taken as a whole can increase the renormalized free energy F={E}{out}-{{TS}}{CFT}-{{Ω }}J, with T,{{Ω }} constants set by {H}B. This latter corollary constitutes a 2nd law for appropriate non-compact AdS event horizons.
NASA Astrophysics Data System (ADS)
Kawamoto, Noboru; Kugo, Taichiro
String theories seem to have created a breakthrough in theoretical physics. At long last a unified theory of all the fundamental interactions, including gravity, looks possible. This, according to theorist Stephen Hawking, will mark the end of theoretical physics as we have known it, since we will then have a single consistent theory within which to explain all natural phenomena from elementary particles to galactic superclusters. Strings themselves are extremely tiny entities, smaller than the Planck scale, which form loops whose vibrational harmonics can be used to model all the standard elementary particles. Of course the mathematical complexities of the theory are daunting, and physicists are still at a very early stage in understanding how strings and their theoretical cousins superstrings can be used. This proceedings volume gives an overview of the intense recent work in the field and reports latest developments.
GENERAL: Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
NASA Astrophysics Data System (ADS)
Yang, Xu-Hua; Sun, Bao; Wang, Bo; Sun, You-Xian
2010-04-01
Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper.
Xun, D.M.; Liu, Q.H.; Zhu, X.M.
2013-11-15
A generalization of Dirac’s canonical quantization scheme for a system with second-class constraints is proposed, in which the fundamental commutation relations are constituted by all commutators between positions, momenta and Hamiltonian, so they are simultaneously quantized in a self-consistent manner, rather than by those between merely positions and momenta which leads to ambiguous forms of the Hamiltonian and the momenta. The application of the generalized scheme to the quantum motion on a torus leads to a remarkable result: the quantum theory is inconsistent if built up in an intrinsic geometric manner, whereas it becomes consistent within an extrinsic examination of the torus as a submanifold in three dimensional flat space with the use of the Cartesian coordinate system. The geometric momentum and potential are then reasonably reproduced. -- Highlights: •A generalization of Dirac’s canonical quantization is proposed for a system with second-class constraints. •Quantum motion on torus surface is explicitly treated to show how Schrödinger formalism is complementary to the Dirac one. •The embedding effect in quantum mechanics is originated from the quantization.
NASA Astrophysics Data System (ADS)
Szymańska, M. H.; Keeling, J.; Littlewood, P. B.
2007-05-01
We study the mean-field theory, and the properties of fluctuations, in an out of equilibrium Bose-Fermi system, across the transition to a quantum condensed phase. The system is driven out of equilibrium by coupling to multiple baths, which are not in equilibrium with each other, and thus drive a flux of particles through the system. We derive the self-consistency condition for a uniform condensed steady state. This condition can be compared both to the laser rate equation and to the Gross-Pitaevskii equation of an equilibrium condensate. We study fluctuations about the steady state and discuss how the multiple baths interact to set the system’s distribution function. In the condensed system, there is a soft phase (Bogoliubov, Goldstone) mode, diffusive at small momenta due to the presence of pump and decay, and we discuss how one may determine the field-field correlation functions properly including such soft phase modes. In the infinite system, the correlation functions differ both from the laser and from an equilibrium condensate; we discuss how in a finite system, the laser limit may be recovered.
Whalley, Lisa; Stone, Daniel; Heard, Dwayne
2014-01-01
In this chapter we discuss some of the recent work directed at further understanding the chemistry of our atmosphere in regions of low NO x , such as forests, where there are considerable emissions of biogenic volatile organic compounds, for example reactive hydrocarbons such as isoprene. Recent field measurements have revealed some surprising results, for example that OH concentrations are measured to be considerably higher than can be understood using current chemical mechanisms. It has also not proven possible to reconcile field measurements of other species, such as oxygenated VOCs, or emission fluxes of isoprene, using current mechanisms. Several complementary approaches have been brought to bear on formulating a solution to this problem, namely field studies using state-of-the-art instrumentation, chamber studies to isolate sub-sections of the chemistry, laboratory studies to measure rate coefficients, product branching ratios and photochemical yields, the development of ever more detailed chemical mechanisms, and high quality ab initio quantum theory to calculate the energy landscape for relevant reactions and to enable the rates of formation of products and intermediates for previously unknown and unstudied reactions to be predicted. The last few years have seen significant activity in this area, with several contrasting postulates put forward to explain the experimental findings, and here we attempt to synthesise the evidence and ideas.
A kinetic theory of diffusion in general relativity with cosmological scalar field
Calogero, Simone
2011-11-01
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario.
Robert R. Wilson Prize II: A Quantum Field Theory Approach to Intrabeam Scattering
NASA Astrophysics Data System (ADS)
Bjorken, James
2017-01-01
My involvement in the intrabeam scattering problem was very brief, from the autumn of 1981 to the summer of 1982. It occurred during my tenure at Fermilab. I entered the subject as an amateur in accelerator theory. But my experience in elementary-particle theory turned out to be of help in advancing the subject.
Homogeneous cosmologies as group field theory condensates
NASA Astrophysics Data System (ADS)
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2014-06-01
We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the `condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
Problem of the Landau Poles in Quantum Field Theory: from N. N. Bogolyubov to the Present Day
NASA Astrophysics Data System (ADS)
Jafarov, R. G.; Agham-Alieva, L. A.; Agha-Kishieva, P. É.; Rahim-zade, S. G.; Mamedova, S. N.; Mutallimov, M. M.
2017-03-01
A review of problems associated with the unphysical Landau pole in propagators of quantum particles is given. Approaches to eliminating this pole within the framework of electrodynamics and effective theories of strongly interacting particles are investigated. The asymptotic behavior at large momenta in the scalar theory ϕ4 in the two-particle (bubble) approximation is investigated. To formulate a calculational model in the two-particle approximation, we use an iterative scheme for solving the Schwinger-Dyson equation in the formalism of a bilocal field source. The main problem is to develop a recipe for numerical analysis of the solutions of the obtained nonlinear equation for the amplitude at small interaction distances (large values of the momentum) for different values of the constant. The nontrivial behavior of the amplitude in the deeply inelastic region of momenta is determined. The positions of the unphysical poles (the Landau poles) in the expression for the amplitude in the deeply inelastic region of momenta are identified.
Weak Quantum Theory: Formal Framework and Selected Applications
Atmanspacher, Harald; Filk, Thomas; Roemer, Hartmann
2006-01-04
Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli.
On the Question of the Causality Condition in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Khokhlov, I. A.
2017-01-01
A mathematically correct generalization of the Bogoliubov microcausality condition to the case of arbitrary points in spacetime is given. The proposed generalized formulation of the microcausality condition is the basis for construction of a scattering matrix not containing ultraviolet divergences.
Finite field-dependent symmetries in perturbative quantum gravity
Upadhyay, Sudhaker
2014-01-15
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also.
Field-theory methods in coagulation theory
Lushnikov, A. A.
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Diehl, S.; Daley, A. J.; Zoller, P.; Baranov, M.
2010-08-01
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a 'continuous supersolid', which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Theory of smeared quantum phase transitions.
Hoyos, José A; Vojta, Thomas
2008-06-20
We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.
NASA Astrophysics Data System (ADS)
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
NASA Astrophysics Data System (ADS)
Raftopoulos, Dionysios G.
Werner Heisenberg's well known requirement that Physical Science ought to occupy itself solely with entities that are both observable and measurable, is almost universally accepted. Starting from the above thesis and accepting Albert Einstein's second fundamental hypothesis, as stated in his historical article "On the Electrodynamics of moving Bodies", we are led to the conclusion that the kinematics of a material point, as measured and described by a localized real-life Observer, always refers not to its present position but rather to the one it occupied at a previous moment in time, which we call Conjugate Position, or Retarded Position according to Richard Feynman. From the experimenter's point of view, only the Conjugate position is important. Thus, the moving entity is observed and measured at a position that is different to the one it occupies now, a conclusion eerily evocative of the "shadows" paradigm in Plato's Cave Allegory. This, i.e. the kinematics of the Conjugate Position, is analytically described by the "Theory of Harmonicity of the Field of Light". Having selected the Projective Space as its Geometrical space of choice, an important conclusion of this theory is that, for a localized Observer, a linearly moving object is possible to appear simultaneously at two different positions and, consequently, at two different states in the Observer's Perceptible Space. This conclusion leads to the formulation of at least two fundamental theorems as well as to a plethora of corollaries all in accordance with the notions of contemporary Quantum Mechanics. A new form of the Unified Field of Light is presented.
Quantum field theory in the space-time of a cosmic string
Linet, B.
1987-01-15
For a massive scalar field in the static cylindrically symmetric space-time describing a cosmic string, we determine explicitly the Euclidean Green's function. We obtain also an alternative local form which allows us to calculate the vacuum energy-momentum tensor. In the case of a conformal scalar field, we carry out completely the calculations.
General model of phospholipid bilayers in fluid phase within the single chain mean field theory.
Guo, Yachong; Pogodin, Sergey; Baulin, Vladimir A
2014-05-07
Coarse-grained model for saturated phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsaturated phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equilibrium and mechanical properties of a range of saturated lipid molecules that differ only in length of their hydrophobic tails and unsaturated (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as saturated lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equilibrium area per lipid correspond to experimentally measured values for each lipid, changing linearly with the length of the tail. The model for unsaturated phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estimation of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable estimates for free energies. The proposed model may further be used for studies of mixtures of lipids, small molecule inclusions, interactions of bilayers with embedded proteins.
Role of dissipation in biasing the vacuum selection in quantum field theory at finite temperature
Freire, F.; Achucarro, A.; Antunes, N.D.; Salmi, P.
2005-08-15
We study the symmetry breaking pattern of an O(4) symmetric model of scalar fields, with both charged and neutral fields, interacting with a photon bath. Nagasawa and Brandenberger argued that in favorable circumstances the vacuum manifold would be reduced from S{sup 3} to S{sup 1}. Here it is shown that a selective condensation of the neutral fields, that are not directly coupled to photons, can be achieved in the presence of a minimal external dissipation, i.e. not related to interactions with a bath. This should be relevant in the early universe or in heavy-ion collisions where dissipation occurs due to expansion.
Cutkosky rules for superstring field theory
NASA Astrophysics Data System (ADS)
Pius, Roji; Sen, Ashoke
2016-10-01
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
Quantum Theory of Antisymmetric Higher Rank Tensor Gauge Field in Higher Dimensional Space-Time
NASA Astrophysics Data System (ADS)
Kimura, T.
1981-01-01
In a higher dimensional space-time, the Lagrangian formalism and the canonical operator formalism of covariant quantization of the antisymmetric tensor gauge field of higher rank are formulated consistently by introducing BRS transformation and Lagrangian multiplier fields From the effective Lagrangian, the numbers of the physical components and the effective ghosts are counted correctly without referring to a special reference frame. The confinement of unphysical components is assured from the viewpoint of the ``quartet mechanism'' of Kugo and Ojima.
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Comments on quantum probability theory.
Sloman, Steven
2014-01-01
Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.
Validity of the minisuperspace approximation: An example from interacting quantum field theory
Sinha, S.; Hu, B.L. )
1991-08-15
We examine the question of the validity of the minisuperspace approximation using the example of an interacting ({lambda}{Phi}{sup 4}) scalar field in a closed Robertson-Walker universe, where the scale factor and the homogeneous mode of the scalar field model the minisuperspace degrees of freedom. We explicitly compute the back reaction of the inhomogeneous modes on the minisuperspace sector using a coarse-grained effective action and show that the minisuperspace approximation is valid only when this back reaction is small.
Gambini, R; Pullin, J
2000-12-18
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the lambda --> infinity limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.
NASA Astrophysics Data System (ADS)
Schuler, Michael; Whitsitt, Seth; Henry, Louis-Paul; Sachdev, Subir; Läuchli, Andreas M.
2016-11-01
The low-energy spectra of many body systems on a torus, of finite size L , are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2 +1 )D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the low-energy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1 /L . We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z2 topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
Schuler, Michael; Whitsitt, Seth; Henry, Louis-Paul; Sachdev, Subir; Läuchli, Andreas M
2016-11-18
The low-energy spectra of many body systems on a torus, of finite size L, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2+1)D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the low-energy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1/L. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z_{2} topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
Solitons in quantum field theory: Magnetic monopoles, black holes, and supersymmetry
NASA Astrophysics Data System (ADS)
Miller, Christopher M.
We show that spherically-symmetric non-extremal black holes can be obtained as solutions to a set of BPS-like first-order equations. Because the Killing spinor equations for a supergravity theory are also first-order, this suggests that supersymmetry may play a hidden role in black hole solutions. We show that in the effective 1 + 1-dimensional action for the spherically-symmetric ansatz, the black hole is a supersymmetric solution. However, we also show that a non-extremal black hole metric cannot admit a Killing spinor, and hence it cannot be a supersymmetric solution of any supergravity theory. Following this result, we present an analysis of massless monopole dynamics. Massless monopoles are manifested as clouds of non-Abelian magnetic charge that surround massive monopoles. Previous analyses have investigated how these clouds interact with massive monopoles, but this calculation is the first to show how massless monopoles interact with one another. Because of the conjectured duality between magnetic monopole moduli spaces and the corresponding moduli spaces of Nahm data, the moduli space approximation tells us that the geodesics on the space of Nahm data will provide a description of the low-energy dynamics of a multi-monopole configuration. We find an implicit expression for the metric on the forty-dimensional space of Nahm data for a configuration of four massive and six massless monopoles in an SU(6) gauge theory---this space will be referred to as a (2, [2], [2], [2], 2) multi-monopole. We then provide the explicit expression for the metric of a four-dimensional totally geodesic subspace, which corresponds to the subspace of axially symmetric configurations contained within the (2, [2], [2], [2], 2) multi-monopole. Once this metric is calculated, it is possible to obtain the geodesics on the resulting subspace via numerical methods. We find two distinct types of massless monopole clouds, which we refer to as SU(4) and Dancer clouds. In a system containing
Quantum Gauge Theories : A True Ghost Story
NASA Astrophysics Data System (ADS)
Scharf, Gunter
2001-03-01
An innovative new treatment of particle physics using quantum gauge theory as its basis If regarded as operator theories, ghost fields play a very important role in quantum gauge theory, which forms the basis of modern particle physics. The author argues that all known forces in nature-electromagnetism, weak and strong forces, and gravity-follow in a unique way from the basic principle of quantum gauge invariance. Using that as a starting point, this volume discusses gauge theories as quantum theories, as part of a streamlined modern approach. The simplicity of using only this one method throughout the book allows the reader a clear understanding of the mathematical structure of nature, while this modern and mathematically well-defined approach elucidates the standard theory of particle physics without overburdening the reader with the full range of various ideas and methods. Though the subject matter requires a basic knowledge of quantum mechanics, the book's unprecedented and uncomplicated coverage will offer readers little difficulty. This revolutionary volume is suitable for graduate students and researchers alike and includes a completely new treatment of gravity as well as important new ideas on massive gauge fields.
Scale invariance, conformality, and generalized free fields
Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; Luty, Markus A.; Prilepina, Valentina
2016-02-16
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum fi eld theories with scale invariance but not conformal invariance. We present an important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen that is the trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.
Scale invariance, conformality, and generalized free fields
Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; ...
2016-02-16
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum fi eld theories with scale invariance but not conformal invariance. We present an important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen that is the trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unlessmore » the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Finally, despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.« less
Elementary Concepts of Quantum Theory
ERIC Educational Resources Information Center
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Local State and Sector Theory in Local Quantum Physics
NASA Astrophysics Data System (ADS)
Ojima, Izumi; Okamura, Kazuya; Saigo, Hayato
2016-06-01
We define a new concept of local states in the framework of algebraic quantum field theory (AQFT). Local states are a natural generalization of states and give a clear vision of localization in the context of QFT. In terms of them, we can find a condition from which follows automatically the famous DHR selection criterion in DHR-DR theory. As a result, we can understand the condition as consequences of physically natural state preparations in vacuum backgrounds. Furthermore, a theory of orthogonal decomposition of completely positive (CP) maps is developed. It unifies a theory of orthogonal decomposition of states and order structure theory of CP maps. Using it, localized version of sectors is formulated, which gives sector theory for local states with respect to general reference representations.
NASA Astrophysics Data System (ADS)
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Quantum mechanics of Proca fields
NASA Astrophysics Data System (ADS)
Zamani, Farhad; Mostafazadeh, Ali
2009-05-01
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
Generalized teleparallel theory
NASA Astrophysics Data System (ADS)
Junior, Ednaldo L. B.; Rodrigues, Manuel E.
2016-07-01
We construct a theory in which the gravitational interaction is described only by torsion, but that generalizes the teleparallel theory still keeping the invariance of local Lorentz transformations in one particular case. We show that our theory falls, in a certain limit of a real parameter, under f(bar{R}) gravity or, in another limit of the same real parameter, under modified f( T) gravity; on interpolating between these two theories it still can fall under several other theories. We explicitly show the equivalence with f(bar{R}) gravity for the cases of a Friedmann-Lemaître-Robertson-Walker flat metric for diagonal tetrads, and a metric with spherical symmetry for diagonal and non-diagonal tetrads. We study four applications, one in the reconstruction of the de Sitter universe cosmological model, for obtaining a static spherically symmetric solution of de Sitter type for a perfect fluid, for evolution of the state parameter ω _{DE}, and for the thermodynamics of the apparent horizon.
Vukmirovic, Nenad; Wang, Lin-Wang
2009-11-10
This review covers the description of the methodologies typically used for the calculation of the electronic structure of self-assembled and colloidal quantum dots. These are illustrated by the results of their application to a selected set of physical effects in quantum dots.
Solving the simplest theory of quantum gravity
NASA Astrophysics Data System (ADS)
Dubovsky, Sergei; Flauger, Raphael; Gorbenko, Victor
2012-09-01
We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, "asymptotic fragility". Asymptotically fragile flows do not originate from a UV fixed point.
Quantum Hamilton-Jacobi theory.
Roncadelli, Marco; Schulman, L S
2007-10-26
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We overcome this difficulty. We show that solutions to the QHJE can be constructed by a simple prescription starting from the propagator of the associated Schrödinger equation. Our result opens the possibility of practical use of quantum Hamilton-Jacobi theory. As an application, we develop a surprising relation between operator ordering and the density of paths around a semiclassical trajectory.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
No extension of quantum theory can have improved predictive power.
Colbeck, Roger; Renner, Renato
2011-08-02
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography.
NASA Astrophysics Data System (ADS)
Maxfield, Travis; Robbins, Daniel; Sethi, Savdeep
2016-11-01
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2, 0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
A Generalized Information Theoretical Model for Quantum Secret Sharing
NASA Astrophysics Data System (ADS)
Bai, Chen-Ming; Li, Zhi-Hui; Xu, Ting-Ting; Li, Yong-Ming
2016-11-01
An information theoretical model for quantum secret sharing was introduced by H. Imai et al. (Quantum Inf. Comput. 5(1), 69-80 2005), which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analyse two kinds of important quantum access structures to illustrate the existence and rationality for the generalized quantum secret sharing schemes and consider the security of the scheme by simple examples.
Generalized SU(2) Proca theory
NASA Astrophysics Data System (ADS)
Allys, Erwan; Peter, Patrick; Rodríguez, Yeinzon
2016-10-01
Following previous works on generalized Abelian Proca theory, also called vector Galileon, we investigate the massive extension of an SU(2) gauge theory, i.e., the generalized SU(2) Proca model, which could be dubbed non-Abelian vector Galileon. This particular symmetry group permits fruitful applications in cosmology such as inflation driven by gauge fields. Our approach consists in building, in an exhaustive way, all the Lagrangians containing up to six contracted Lorentz indices. For this purpose, and after identifying by group theoretical considerations all the independent Lagrangians which can be written at these orders, we consider the only linear combinations propagating 3 degrees of freedom and having healthy dynamics for their longitudinal mode, i.e., whose pure Stückelberg contribution turns into the SU(2) multi-Galileon dynamics. Finally, and after having considered the curved space-time expansion of these Lagrangians, we discuss the form of the theory at all subsequent orders.
Maxwell-Garnett effective medium theory: Quantum nonlocal effects
Moradi, Afshin
2015-04-15
We develop the Maxwell-Garnett theory for the effective medium approximation of composite materials with metallic nanoparticles by taking into account the quantum spatial dispersion effects in dielectric response of nanoparticles. We derive a quantum nonlocal generalization of the standard Maxwell-Garnett formula, by means the linearized quantum hydrodynamic theory in conjunction with the Poisson equation as well as the appropriate additional quantum boundary conditions.
Is quantum theory predictably complete?
NASA Astrophysics Data System (ADS)
Kupczynski, M.
2009-07-01
Quantum theory (QT) provides statistical predictions for various physical phenomena. To verify these predictions a considerable amount of data has been accumulated in the 'measurements' performed on the ensembles of identically prepared physical systems or in the repeated 'measurements' on some trapped 'individual physical systems'. The outcomes of these measurements are, in general, some numerical time series registered by some macroscopic instruments. The various empirical probability distributions extracted from these time series were shown to be consistent with the probabilistic predictions of QT. More than 70 years ago the claim was made that QT provided the most complete description of 'individual' physical systems and outcomes of the measurements performed on 'individual' physical systems were obtained in an intrinsically random way. Spin polarization correlation experiments (SPCEs), performed to test the validity of Bell inequalities, clearly demonstrated the existence of strong long-range correlations and confirmed that the beams hitting far away detectors somehow preserve the memory of their common source which would be destroyed if the individual counts of far away detectors were purely random. Since the probabilities describe the random experiments and are not the attributes of the 'individual' physical systems, the claim that QT provides a complete description of 'individual' physical systems seems not only unjustified but also misleading and counter productive. In this paper, we point out that we even do not know whether QT is predictably complete because it has not been tested carefully enough. Namely, it was not proven that the time series of existing experimental data did not contain some stochastic fine structures that could have been averaged out by describing them in terms of the empirical probability distributions. In this paper, we advocate various statistical tests that could be used to search for such fine structures in the data and to
Superconducting quantum circuits theory and application
NASA Astrophysics Data System (ADS)
Deng, Xiuhao
states. The model and toolbox are engineered with a superconducting quantum circuit where two superconducting resonators are coupled via the UQDP circuit. Using fourth order perturbation theory one can realize a complete set of quantum operations between these two photon modes. This helps open a new field to treat photon modes as qubits. Additional, a three-wave mixing scheme using phase qubits permits one to engineer the coupling Hamiltonian using a phase qubit as a tunable coupler. Along with Feynman's idea using quantum to simulate quantum, superconducting quantum simulators have been studied intensively recently. Taking the advantage of mesoscopic size of superconducting circuit and local tunability, we came out the idea to simulate quantum phase transition due to disorder. Our first paper was to propose a superconducting quantum simulator of Bose-Hubbard model to do site-wise manipulation and observe Mott-insulator to superfluid phase transition. The side-band cooling of an array of superconducting resonators is solved after the paper was published. In light of the developed technology in manipulating quantum information with superconducting circuit, one can couple other quantum oscillator system to superconducting resonators in order manipulation of its quantum states or parametric amplification of weak quantum signal. A theory that works for different coupling schemes has been studied in chapter 5. This will be a platform for further research.
A general waveguide circuit theory
NASA Astrophysics Data System (ADS)
Marks, Roger B.; Williams, Dylan F.
1992-10-01
This work generalizes and extends the classical circuit theory of electromagnetic waveguides. Unlike the conventional theory, the present formulation applies to all waveguides composed of linear, isotropic material, even those involving lossy conductors and hybrid mode fields, in a fully rigorous way. Special attention is given to distinguishing the traveling waves, constructed with respect to a well-defined characteristic impedance, from a set of pseudo-waves, defined with respect to an arbitrary reference impedance. Matrices characterizing a linear circuit are defined, and relationships among them, some newly discovered, are derived. New ramifications of reciprocity are developed. Measurement of various network parameters is given extensive treatment.
Republication of: Exact solutions of the field equations of the general theory of relativity
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Ehlers, Jürgen; Kundt, Wolfgang
2009-09-01
This is an English translation of a paper by Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, first published in 1960. The original paper was part 1 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (The other parts of the series will be printed as Golden Oldies in the future.) The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. It is accompanied by an editorial note written by G. F. R. Ellis, and by the biographies of the authors: P. Jordan (written by A. Krasiński) and W. Kundt (written by himself). The biography of J. Ehlers is contained elsewhere in the same issue of GRG, which is devoted to his memory.
Propensity, Probability, and Quantum Theory
NASA Astrophysics Data System (ADS)
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Basing quantum theory on information processing
NASA Astrophysics Data System (ADS)
Barnum, Howard
2008-03-01
I consider information-based derivations of the quantum formalism, in a framework encompassing quantum and classical theory and a broad spectrum of theories serving as foils to them. The most ambitious hope for such a derivation is a role analogous to Einstein's development of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of this, it could still provide a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, helping guide the search for new quantum algorithms and protocols. I summarize the convex operational framework for theories, and discuss information-processing in theories therein. Results include the fact that information that can be obtained without disturbance is inherently classical, generalized no-cloning and no-broadcasting theorems, exponentially secure bit commitment in all non-classical theories without entanglement, properties of theories that allow teleportation, and properties of theories that allow ``remote steering'' of ensembles using entanglement. Joint work with collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner.
Information theory, spectral geometry, and quantum gravity.
Kempf, Achim; Martin, Robert
2008-01-18
We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
NASA Astrophysics Data System (ADS)
Grosse, Harald; Wulkenhaar, Raimar
2014-08-01
We study quartic matrix models with partition function exp(trace). The integral is over the space of Hermitean -matrices, the external matrix E encodes the dynamics, is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing β-function. As the main application we prove that Euclidean -quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for the same spectrum as the Laplace operator in four dimensions. Using the theory of singular integral equations of Carleman type we compute (for and after renormalisation of ) the free energy density (1/volume) log exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which in subsequent work is verified for coupling constants.
Quantum dynamics in strong fluctuating fields
NASA Astrophysics Data System (ADS)
Goychuk, Igor; Hänggi, Peter
state fluctuations531 2.3. Averaging the quantum propagator533 2.3.1. Kubo oscillator535 2.3.2. Averaged dynamics of two-level quantum systems exposed to two-state stochastic fields537 2.4. Projection operator method: a primer5403. Two-state quantum dynamics in periodic fields542 3.1. Coherent destruction of tunnelling542 3.2. Driving-induced tunnelling oscillations (DITO)5434. Dissipative quantum dynamics in strong time-dependent fields544 4.1. General formalism544 4.1.1. Weak-coupling approximation545 4.1.2. Markovian approximation: Generalised Redfield Equations5475. Application I: Quantum relaxation in driven, dissipative two-level systems548 5.1. Decoupling approximation for fast fluctuating energy levels550 5.1.1. Control of quantum rates551 5.1.2. Stochastic cooling and inversion of level populations552 5.1.3. Emergence of an effective energy bias553 5.2. Quantum relaxation in strong periodic fields554 5.3. Approximation of time-dependent rates554 5.4. Exact averaging for dichotomous Markovian fluctuations5556. Application II: Driven electron transfer within a spin-boson description557 6.1. Curve-crossing problems with dissipation558 6.2. Weak system-bath coupling559 6.3. Beyond weak-coupling theory: Strong system-bath coupling563 6.3.1. Fast fluctuating energy levels565 6.3.2. Exact averaging over dichotomous fluctuations of the energy levels566 6.3.3. Electron transfer in fast oscillating periodic fields567 6.3.4. Dichotomously fluctuating tunnelling barrier5687. Quantum transport in dissipative tight-binding models subjected tostrong external fields569 7.1. Noise-induced absolute negative mobility571 7.2. Dissipative quantum rectifiers573 7.3. Limit of vanishing dissipation575 7.4. Case of harmonic mixing drive5758. Summary576Acknowledgements578References579
Reasonable fermionic quantum information theories require relativity
NASA Astrophysics Data System (ADS)
Friis, Nicolai
2016-03-01
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.
Classical field approach to quantum weak measurements.
Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco
2014-03-21
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.
Objectivism, Naturalism, and the Revision of Quantum Theory.
NASA Astrophysics Data System (ADS)
Cordero-Lecca, Alberto
Because of its remarkable predictive power and general scientific fertility, there is a temptation to take quantum theory (QT) seriously as the best statement science can currently make about the world. But when the consequences of the theory are drawn out, they reveal strange, indeed paradoxical, possibilities of superpositions. QT seems to imply that the entire world, not just the world of microparticles, is considerably less 'objective' than common intuition suggests. To what extent, if any, however, is QT at odds with a reasonable conception of scientific objectivity? I argue that, far from committing us to paradox, quantum physics actually encourages us to think of the world in strong objectivist naturalist terms. After examining various influential programs in the field, I propose an approach to the foundational problems of QT which is less 'theory-down' than usual. In particular, I argue that recent studies of metastable states both support a strongly objectivist formulation of quantum dynamics and direct us to a natural generalization and revision of QT. The model that thus emerges turns out to be a member of the stochastic family of QT revisions developed by Ghirardi, Rimini & Weber, Pearle, and Gisin, which are theories that preserve the level of peaceful coexistence with special relativity that standard QT and its field-theoretic generalizations have. The specific proposal advanced in this monograph focuses on spontaneous transitions to bound energy states. No ad hoc parameters are assumed. The resulting approach seems able to explain successful working-level talk about such topics as quantum jumps, localization by interaction with macrosystems, standard measurement rules, all this without denying the existence of either quantum superpositions or EPR correlations.
Holism, physical theories and quantum mechanics
NASA Astrophysics Data System (ADS)
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Operational quantum theory without predefined time
NASA Astrophysics Data System (ADS)
Oreshkov, Ognyan; Cerf, Nicolas J.
2016-07-01
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures.
NASA Astrophysics Data System (ADS)
Arfi, Badredine
2007-02-01
Most game-theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis. This paper explores the effects of non-independence on strategic interaction. Two types of non-independence effects are considered. First, the paper considers subjective non-independence at the level of the individual actor by looking at how choice ambivalence shapes the decision-making process. Specifically, how do alternative individual choices superpose with one another to “constructively/destructively” shape each other's role within an actor's decision-making process? This process is termed as quantum superposition of alternative choices. Second, the paper considers how inter-subjective non-independence across actors engenders collective strategies among two or more interacting actors. This is termed as quantum entanglement of strategies. Taking into account both types of non-independence effect makes possible the emergence of a new collective equilibrium, without assuming signaling, prior “contract” agreement or third-party moderation, or even “cheap talk”. I apply these ideas to analyze the equilibrium possibilities of a situation wherein N actors play a quantum social game of cooperation. I consider different configurations of large- N quantum entanglement using the approach of density operator. I specifically consider the following configurations: star-shaped, nearest-neighbors, and full entanglement.
Quantum walks and non-Abelian discrete gauge theory
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Di Molfetta, Giuseppe; Brachet, Marc; Debbasch, Fabrice
2016-07-01
A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N ) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N ) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N ) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1 ) Maxwell fields and SU(N ) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2 ) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.
Pastore, S.; Wiringa, Robert B.; Pieper, Steven C.; Schiavilla, Rocco
2014-08-01
We report quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30\\% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with the empirical mixing coefficients to compare to experiment. In general, we find that transitions between states that have the same dominant spatial symmetry are in decent agreement with experiment, but those transitions between different spatial symmetries are often significantly underpredicted.
Generalized Entanglement and Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Somma, Rolando; Barnum, Howard; Knill, Emanuel; Ortiz, Gerardo; Viola, Lorenzo
2006-07-01
Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.
Generalized Entanglement and Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Somma, Rolando; Barnum, Howard; Knill, Emanuel; Ortiz, Gerardo; Viola, Lorenzo
Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.
NASA Technical Reports Server (NTRS)
Li, Xi-Zeng; Su, Bao-Xia
1996-01-01
It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations in this process are also presented.
2013-02-15
Universiti Teknikal Malaysia Melaka in Malaysia. The project was then used to partially support a new PhD student, Mr Shanon Vuglar (who is a former...method based on cascade realization of quantum systems is used and a conference and journal paper have been produced. In another approach, a method...based on singular perturbation is used and a conference and journal paper have resulted. This work was extended by the graduate student Shanon Vuglar to
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
Solitons in generalized Galileon theories
NASA Astrophysics Data System (ADS)
Carrillo González, Mariana; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark
2016-12-01
We consider the existence and stability of solitons in generalized Galileons, scalar-field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons exist in a single Galileon theory using an argument invoking the existence of zero modes for the perturbations. Here we analyze the applicability of this argument to generalized Galileons and discuss how this may be avoided by having potential terms in the energy functional for the perturbations or by including time dependence. Given the presence of potential terms in the Lagrangian for the perturbations, we find that stable, static solitons are not ruled out in conformal and (anti-)de Sitter Galileons. For the case of Dirac-Born-Infeld and conformal Galileons, we find that solitonic solutions moving at the speed of light exist, the former being stable and the latter unstable if the background soliton satisfies a certain condition.
NASA Astrophysics Data System (ADS)
Shebeko, A.
2013-12-01
The clothing procedure, put forward in quantum field theory by Greenberg and Schweber, is applied for the description of nucleon-nucleon ( N- N) scattering below the pion production threshold and deuteron properties. We consider pseudoscalar ( π and η), vector ( ρ and ω) and scalar ( δ and σ) meson fields interacting with N and ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. We will also show a worked example where the UCTs method is used in the framework of a gauge-independent field-theoretical treatment of electromagnetic interactions of deuterons (bound systems).
Generalized potentials for a mean-field density functional theory of a three-phase contact line
NASA Astrophysics Data System (ADS)
Lin, Chang-You; Widom, Michael; Sekerka, Robert F.
2013-07-01
We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.011120 85, 011120 (2012)], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear functions that vanish at edges and vertices of the small triangle, yielding potentials in the form of quartic polynomials. We find that a subset of such potentials has simple analytic far-field solutions and is a linear transformation of our original potential. By scaling, we can relate their solutions to those of our original potential. For special cases, the lengths of the sides of the small triangle are proportional to the corresponding interfacial tensions. For the case of equal interfacial tensions, we calculate a line tension that is proportional to the area of the small triangle.
Langevin description of nonequilibrium quantum fields
NASA Astrophysics Data System (ADS)
Gautier, F.; Serreau, J.
2012-12-01
We consider the nonequilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral two-point functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly nonlocal, thereby questioning the possibility of a local description. We show that despite this fact, there is a finite time range during which a local description is accurate. This requires the theory to be (effectively) weakly coupled. We illustrate the use of such a local description for studies of decoherence and entropy production in quantum field theory.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.
Plotnitsky, Arkady
2016-05-28
Taking as its point of departure the discovery of the Higgs boson, this article considers quantum theory, including quantum field theory, which predicted the Higgs boson, through the combined perspective of quantum information theory and the idea of technology, while also adopting anon-realistinterpretation, in 'the spirit of Copenhagen', of quantum theory and quantum phenomena themselves. The article argues that the 'events' in question in fundamental physics, such as the discovery of the Higgs boson (a particularly complex and dramatic, but not essentially different, case), are made possible by the joint workings of three technologies: experimental technology, mathematical technology and, more recently, digital computer technology. The article will consider the role of and the relationships among these technologies, focusing on experimental and mathematical technologies, in quantum mechanics (QM), quantum field theory (QFT) and finite-dimensional quantum theory, with which quantum information theory has been primarily concerned thus far. It will do so, in part, by reassessing the history of quantum theory, beginning with Heisenberg's discovery of QM, in quantum-informational and technological terms. This history, the article argues, is defined by the discoveries of increasingly complex configurations of observed phenomena and the emergence of the increasingly complex mathematical formalism accounting for these phenomena, culminating in the standard model of elementary-particle physics, defining the current state of QFT.
A Topos for Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas
2009-10-01
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos {mathcal{T}(A)} in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra {A} . According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum {\\underline{Σ}(A)} in {mathcal{T}(A)} , which in our approach plays the role of the quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on {\\underline{Σ}} , and self-adjoint elements of A define continuous functions (more precisely, locale maps) from {\\underline{Σ}} to Scott’s interval domain. Noting that open subsets of {\\underline{Σ}(A)} correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos {mathcal{T}(A)}. These results were inspired by the topos-theoretic approach to quantum physics proposed by Butterfield and Isham, as recently generalized by Döring and Isham.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
General Systems Theory and Instructional Design.
ERIC Educational Resources Information Center
Salisbury, David F.
The use of general systems theory in the field of instructional systems design (ISD) is explored in this paper. Drawing on work by Young, the writings of 12 representative ISD writers and researchers were surveyed to determine the use of 60 general systems theory concepts by the individual authors. The average number of concepts used by these…
Large Quantum Gravity Effects: Unforeseen Limitations of the Classical Theory
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay
1996-12-01
Three-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axisymmetry. The solution is used to probe several quantum gravity issues. In particular, it is found that if there is an electromagnetic wave of Planckian frequency even with such low amplitude that the curvature of the classical solution is small, the uncertainty in the quantum metric can be very large. More generally, the quantum fluctuations in the geometry are large unless the number and frequency of photons satisfy the inequality N\\(ħGω\\)2<<1. Results hold also for a sector of the four-dimensional theory (consisting of Einstein-Rosen gravitational waves).
Variational methods for field theories
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
1986-09-01
The thesis is presented in four parts dealing with field theory models: Periodic Quantum Electrodynamics (PQED) in (2+1) dimensions, free scalar field theory in (1+1) dimensions, the Quantum XY model in (1+1) dimensions, and the (1+1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. Free field theory is used as a laboratory for a new variational blocking truncation approximation, in which the high frequency modes in a block are truncated to wave functions that depend on the slower background model (Born Oppenheimer approximation). For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. In the 4th part, the transfer matrix method is used to find a good (non blocking) trial ground state for the Ising model in a transverse magnetic field in (1+1) dimensions.
Quantum optimal control theory in the linear response formalism
Castro, Alberto; Tokatly, I. V.
2011-09-15
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.
Formalism and Interpretation in Quantum Theory
NASA Astrophysics Data System (ADS)
Wilce, Alexander
2010-04-01
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.
The Global versus Local Hamiltonian Description of Quantum Input-Output Theory
NASA Astrophysics Data System (ADS)
Gough, John
2015-06-01
The aim of this paper is to derive the global Hamiltonian form for a quantum system and bath, or more generally a quantum network with multiple quantum input field connections, based on the local descriptions. We give a new simple argument which shows that the global Hamiltonian for a single Markov component arises as the singular perturbation of the free translation operator. We show that the Fermi analogue takes an equivalent form provided the parity of the coefficients is correctly specified. This allows us to immediately extend the theory of quantum feedback networks to Fermi systems.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1998-06-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1997-02-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.
2015-11-15
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Landau ghost pole problem in quantum field theory: From 50th of last century to the present day
NASA Astrophysics Data System (ADS)
Jafarov, Rauf G.; Mutallimov, Mutallim M.
2016-03-01
In this paper we present our results of the investigation of asymptotical behavior of amplitude at short distances in four-dimensional scalar field theory with ϕ4 interaction. To formulate of our calculating model - two-particle approximation of the mean-field expansion we have used an Rochev's iteration scheme of solution of the Schwinger-Dyson equations with the fermion bilocal source. We have considered the nonlinear integral equations in deep-inelastic region of momenta. As result we have a non-trivial behavior of amplitude at large momenta.
Cosmology in generalized Proca theories
NASA Astrophysics Data System (ADS)
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-06-01
We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.
Objectivism, naturalism, and the revision of quantum theory
Cordero-Lecca, A.
1992-01-01
Because of its remarkable predictive power and general scientific fertility, there is a temptation to take quantum theory (QT) seriously as the best statement science can currently make about the world. But when the consequences of the theory are draw out, they reveal strange, indeed paradoxical, possibilities of superpositions. QT seems to imply that the entire world, not just the world of microparticles, is considerably less [open quotes]objective[close quotes] than common intuition suggests. To what extent, if any, however, is QT at odds with a reasonable conception of scientific objectivity The author argues that, far from committing us to paradox, quantum physics actually encourages us to think of the world in strong objectivist naturalist terms. After examining various influential programs in the field, An approach to the foundational problems of QT which is less [open quotes]theory-down[close quotes] than usual is proposed. In particular, the author argues that recent studies of metastable states both support a strongly objectivist formulation and revision of QT. The model that thus emerges turns out to be a member of the stochastic family of QT revisions developed by Ghirardi, Rimini Weber, Pearle, and Gisin, which are theories that preserve the level of peaceful coexistence with special relativity that standard QT and its field-theoretic generalizations have. The specific-proposal advanced in this monograph focuses on spontaneous transitions to bound energy states. No ad hoc parameters are assumed. The resulting approach seems able to explain successful working-level talk about such topics as quantum jumps, localization by interaction with macrosystems, standard measurement rules, all this without denying the existence of either quantum superpositions or EPR correlations.
Transition operators in electromagnetic-wave diffraction theory - General theory
NASA Technical Reports Server (NTRS)
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
Nonlocal microscopic theory of quantum friction between parallel metallic slabs
Despoja, Vito
2011-05-15
We present a new derivation of the friction force between two metallic slabs moving with constant relative parallel velocity, based on T=0 quantum-field theory formalism. By including a fully nonlocal description of dynamically screened electron fluctuations in the slab, and avoiding the usual matching-condition procedure, we generalize previous expressions for the friction force, to which our results reduce in the local limit. Analyzing the friction force calculated in the two local models and in the nonlocal theory, we show that for physically relevant velocities local theories using the plasmon and Drude models of dielectric response are inappropriate to describe friction, which is due to excitation of low-energy electron-hole pairs, which are properly included in nonlocal theory. We also show that inclusion of dissipation in the nonlocal electronic response has negligible influence on friction.
NASA Astrophysics Data System (ADS)
Brown, Eric G.; Louko, Jorma
2015-08-01
We present and utilize a simple formalism for the smooth creation of boundary conditions within relativistic quantum field theory. We consider a massless scalar field in (1 + 1)-dimensional flat spacetime and imagine smoothly transitioning from there being no boundary condition to there being a two-sided Dirichlet mirror. The act of doing this, expectantly, generates a flux of real quanta that emanates from the mirror as it is being created. We show that the local stress-energy tensor of the flux is finite only if an infrared cutoff is introduced, no matter how slowly the mirror is created, in agreement with the perturbative results of Obadia and Parentani. In the limit of instaneous mirror creation the total energy injected into the field becomes ultraviolet divergent, but the response of an Unruh-DeWitt particle detector passing through the infinite burst of energy nevertheless remains finite. Implications for vacuum entanglement extraction and for black hole firewalls are discussed.
Quantum phenomena and the zeropoint radiation field
NASA Astrophysics Data System (ADS)
de La Peña, L.; Cetto, A. M.
1994-06-01
The stationary solutions for a bound electron immersed in the random zeropoint radiation field of stochastic electrodynamics are studied, under the assumption that the characteristic Fourier frequencies of these solutions are not random. Under this assumption, the response of the particle to the field is linear and does not mix frequencies, irrespectively of the form of the binding force; the fluctuations of the random field fix the scale of the response. The effective radiation field that supports the stationary states of motion is no longer the free vacuum field, but a modified form of it with new statistical properties. The theory is expressed naturally in terms of matrices (or operators), and it leads to the Heisenberg equations and the Hilbert space formalism of quantum mechanics in the radiationless approximation. The connection with the poissonian formulation of stochastic electrodynamics is also established. At the end we briefly discuss a few important aspects of quantum mechanics which the present theory helps to clarify.
Quantum theory of the dielectric constant of a magnetized plasma and astrophysical applications. I.
NASA Technical Reports Server (NTRS)
Canuto, V.; Ventura, J.
1972-01-01
A quantum mechanical treatment of an electron plasma in a constant and homogeneous magnetic field is considered, with the aim of (1) defining the range of validity of the magnetoionic theory (2) studying the deviations from this theory, in applications involving high densities, and intense magnetic field. While treating the magnetic field exactly, a perturbation approach in the photon field is used to derive general expressions for the dielectric tensor. Numerical estimates on the range of applicability of the magnetoionic theory are given for the case of the 'one-dimensional' electron gas, where only the lowest Landau level is occupied.
Resonance fluorescence from an asymmetric quantum dot dressed by a bichromatic electromagnetic field
NASA Astrophysics Data System (ADS)
Kryuchkyan, G. Yu.; Shahnazaryan, V.; Kibis, O. V.; Shelykh, I. A.
2017-01-01
We present the theory of resonance fluorescence from an asymmetric quantum dot driven by a two-component electromagnetic field with two different frequencies, polarizations, and amplitudes (bichromatic field) in the regime of strong light-matter coupling. It follows from the elaborated theory that the broken inversion symmetry of the driven quantum system and the bichromatic structure of the driving field result in unexpected features of the resonance fluorescence, including the infinite set of Mollow triplets, the quench of fluorescence peaks induced by the dressing field, and the oscillating behavior of the fluorescence intensity as a function of the dressing field amplitude. These quantum phenomena are of general physical nature and, therefore, can take place in various double-driven quantum systems with broken inversion symmetry.
‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern-Simons theory
NASA Astrophysics Data System (ADS)
Majhi, Abhishek; Majumdar, Parthasarathi
2014-10-01
We articulate the fact that the loop quantum gravity (LQG) description of the quantum macrostates of black hole horizons, modeled as quantum isolated horizons (QIHs), is completely characterized in terms of two independent integer-valued ‘quantum hairs’, viz, the coupling constant (k) of the quantum SU(2) Chern-Simons (CS) theory describing QIH dynamics, and the number of punctures (N) produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the CS fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this CS theory using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semiclassical input from general relativity vis-a-vis the functional dependence of the isolated horizon mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein-Hawking area law relates these two parameters (as an equilibrium ‘equation of state’), and consequently allows the Barbero-Immirzi parameter to take any real and positive value depending on the value of k/N. The logarithmic correction to the area law obtained a decade ago by R Kaul and one of us (PM), ensues straightforwardly, with precisely the coefficient -3/2, making it a signature of the LQG approach to black hole entropy.
Singularities in a scalar field quantum cosmology
NASA Astrophysics Data System (ADS)
Lemos, Nivaldo A.
1996-04-01
The quantum theory of a spatially flat Friedmann-Robertson-Walker universe with a massless scalar field as the source is further investigated. The classical model is singular and in the framework of a genuine canonical quantization (Arnowitt-Deser-Misner formalism) a discussion is made of the cosmic evolution, particularly of the quantum gravitational collapse problem. It is shown that in a matter-time gauge such that time is identified with the scalar field the classical model is singular either at t=-∞ or at t=+∞, but the quantum model is nonsingular. The latter behavior disproves a conjecture according to which quantum cosmological singularities are predetermined on the classical level by the choice of time.
Noncommutative Quantum Scalar Field Cosmology
Diaz Barron, L. R.; Lopez-Dominguez, J. C.; Sabido, M.; Yee, C.
2010-07-12
In this work we study noncommutative Friedmann-Robertson-Walker (FRW) cosmology coupled to a scalar field endowed with an exponential potential. The quantum scenario is analyzed in the Bohmian formalism of quantum trajectories to investigate the effects of noncommutativity in the evolution of the universe.
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
NASA Astrophysics Data System (ADS)
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
NASA Astrophysics Data System (ADS)
Gagatsos, Christos N.; Karanikas, Alexandros I.; Kordas, Georgios; Cerf, Nicolas J.
2016-02-01
In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.
Ramanantoanina, Harry; Urland, Werner; Cimpoesu, Fanica; Daul, Claude
2013-09-07
Herein we present a Ligand Field Density Functional Theory (LFDFT) based methodology for the analysis of the 4f(n)→ 4f(n-1)5d(1) transitions in rare earth compounds and apply it for the characterization of the 4f(2)→ 4f(1)5d(1) transitions in the quantum cutter Cs2KYF6:Pr(3+) with the elpasolite structure type. The methodological advances are relevant for the analysis and prospection of materials acting as phosphors in light-emitting diodes. The positions of the zero-phonon energy corresponding to the states of the electron configurations 4f(2) and 4f(1)5d(1) are calculated, where the praseodymium ion may occupy either the Cs(+)-, K(+)- or the Y(3+)-site, and are compared with available experimental data. The theoretical results show that the occupation of the three undistorted sites allows a quantum-cutting process. However size effects due to the difference between the ionic radii of Pr(3+) and K(+) as well as Cs(+) lead to the distortion of the K(+)- and the Cs(+)-site, which finally exclude these sites for quantum-cutting. A detailed discussion about the origin of this distortion is also described.
BRST symmetry in the general gauge theories
NASA Astrophysics Data System (ADS)
Hyuk-Jae, Lee; Jae, Hyung, Yee
1994-01-01
By using the residual gauge symmetry interpretation of BRST invariance we have constructed a new BRST formulation for general gauge theories including those with open algebras. For theories with open gauge algebra the formulation leads to a BRST invariant effective action which does not contain any higher order terms in the ghost fields.
Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits
Merkli, M.; Berman, G. P.; Sigal, I. M.
2010-01-01
We describe our recenmore » t results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N -level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times t ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.« less
Propagation in polymer parameterised field theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
2017-01-01
The Hamiltonian constraint operator in loop quantum gravity acts ultralocally. Smolin has argued that this ultralocality seems incompatible with the existence of a quantum dynamics which propagates perturbations between macroscopically seperated regions of quantum geometry. We present evidence to the contrary within an LQG type ‘polymer’ quantization of two dimensional parameterised field theory (PFT). PFT is a generally covariant reformulation of free field propagation on flat spacetime. We show explicitly that while, as in LQG, the Hamiltonian constraint operator in PFT acts ultralocally, states in the joint kernel of the Hamiltonian and diffeomorphism constraints of PFT necessarily describe propagation effects. The particular structure of the finite triangulation Hamiltonian constraint operator plays a crucial role, as does the necessity of imposing (the continuum limit of) its kinematic adjoint as a constraint. Propagation is seen as a property encoded by physical states in the kernel of the constraints rather than that of repeated actions of the finite triangulation Hamiltonian constraint on kinematic states. The analysis yields robust structural lessons for putative constructions of the Hamiltonian constraint in LQG for which ultralocal action co-exists with a description of propagation effects by physical states.
Extension of Loop Quantum Gravity to f(R) Theories
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong; Ma, Yongge
2011-04-01
The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
Extension of loop quantum gravity to f(R) theories.
Zhang, Xiangdong; Ma, Yongge
2011-04-29
The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
General polygamy inequality of multiparty quantum entanglement
NASA Astrophysics Data System (ADS)
Kim, Jeong San
2012-06-01
Using entanglement of assistance, we establish a general polygamy inequality of multiparty entanglement in arbitrary-dimensional quantum systems. For multiparty closed quantum systems, we relate our result with the monogamy of entanglement, and clarify that the entropy of entanglement bounds both monogamy and polygamy of multiparty quantum entanglement.
Understanding Quantum Numbers in General Chemistry Textbooks
ERIC Educational Resources Information Center
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
NASA Astrophysics Data System (ADS)
Kundt, Wolfgang; Trümper, Manfred
2016-04-01
This is an English translation of a paper by Wolfgang Kundt and Manfred Trümper, first published in 1962 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was the last of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (All the other parts of the series have already been re-published as Golden Oldies.) This fifth contribution summarizes key points of the earlier papers and applies them, in particular results from papers II and IV in the series, in the context of the propagation of gravitational radiation when matter is present. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Malcolm A.H. MacCallum and by a brief autobiography of Manfred Trümper.
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Multipartite non-locality and entanglement signatures of a field-induced quantum phase transition
NASA Astrophysics Data System (ADS)
Batle, Josep; Alkhambashi, Majid; Farouk, Ahmed; Naseri, Mosayeb; Ghoranneviss, Mahmood
2017-02-01
Quantum correlation measures are limited in practice to a few number of parties, since no general theory is still capable of reaching the thermodynamic limit. In the present work we study entanglement and non-locality for a cluster of spins belonging to a compound that displays a magnetocaloric effect. A quantum phase transition (QPT) is induced by an external magnetic field B, in such a way that the corresponding quantum fluctuations are reproduced at a much smaller scale than the experimental outcomes, and then described by means of the aforementioned quantum measures.
Prequantum classical statistical field theory: background field as a source of everything?
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2011-07-01
Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's "double solution" approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special "prequantum fields": the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the "photonic field" (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of "vacuum fluctuations") might play the role of a source of such pulses, i.e., the source of everything.
The statistical theory of quantum dots
NASA Astrophysics Data System (ADS)
Alhassid, Y.
2000-10-01
A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron's dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between one-body chaos, quantum interference, and electron-electron interactions. The conductance through such dots displays mesoscopic fluctuations as a function of gate voltage, magnetic field, and shape deformation. The techniques used to describe these fluctuations include semiclassical methods, random-matrix theory, and the supersymmetric nonlinear σ model. In open dots, the approximation of noninteracting quasiparticles is justified, and electron-electron interactions contribute indirectly through their effect on the dephasing time at finite temperature. In almost-closed dots, where conductance occurs by tunneling, the charge on the dot is quantized, and electron-electron interactions play an important role. Transport is dominated by Coulomb blockade, leading to peaks in the conductance that at low temperatures provide information on the dot's ground-state properties. Several statistical signatures of electron-electron interactions have been identified, most notably in the dot's addition spectrum. The dot's spin, determined partly by exchange interactions, can also influence the fluctuation properties of the conductance. Other mesoscopic phenomena in quantum dots that are affected by the charging energy include the fluctuations of the cotunneling conductance and mesoscopic Coulomb blockade.
General relativistic effects in quantum interference of “clocks”
NASA Astrophysics Data System (ADS)
Zych, M.; Pikovski, I.; Costa, F.; Brukner, Č.
2016-06-01
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of “clocks”, which aim to test novel quantum effects that arise from time dilation. “Clock” interference experiments could be realised with atoms or photons in near future laboratory experiments.
On fractional quantum Hall solitons in ABJM-like theory
NASA Astrophysics Data System (ADS)
Belhaj, Adil
2011-11-01
Using D-brane physics, we study fractional quantum Hall solitons (FQHS) in ABJM-like theory in terms of type IIA dual geometries. In particular, we discuss a class of Chern-Simons (CS) quivers describing FQHS systems at low energy. These CS quivers come from R-R gauge fields interacting with D6-branes wrapped on 4-cycles, which reside within a blown up CP3 projective space. Based on the CS quiver method and mimicking the construction of del Pezzo surfaces in terms of CP2, we first give a model which corresponds to a single layer model of FQHS system, then we propose a multi-layer system generalizing the doubled CS field theory, which is used in the study of topological defect in graphene.
Quantum oscillations without magnetic field
NASA Astrophysics Data System (ADS)
Liu, Tianyu; Pikulin, D. I.; Franz, M.
2017-01-01
When the magnetic field B is applied to a metal, nearly all observable quantities exhibit oscillations periodic in 1 /B . Such quantum oscillations reflect the fundamental reorganization of electron states into Landau levels as a canonical response of the metal to the applied magnetic field. We predict here that, remarkably, in the recently discovered Dirac and Weyl semimetals, quantum oscillations can occur in the complete absence of magnetic field. These zero-field quantum oscillations are driven by elastic strain which, in the space of the low-energy Dirac fermions, acts as a chiral gauge potential. We propose an experimental setup in which the strain in a thin film (or nanowire) can generate a pseudomagnetic field b as large as 15 T and demonstrate the resulting de Haas-van Alphen and Shubnikov-de Haas oscillations periodic in 1 /b .
Generalized quantum interference of correlated photon pairs
Kim, Heonoh; Lee, Sang Min; Moon, Han Seb
2015-01-01
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source. PMID:25951143
Complementarity and entanglement in quantum information theory
NASA Astrophysics Data System (ADS)
Tessier, Tracey Edward
This research investigates two inherently quantum mechanical phenomena, namely complementarity and entanglement, from an information-theoretic perspective. Beyond philosophical implications, a thorough grasp of these concepts is crucial for advancing our understanding of foundational issues in quantum mechanics, as well as in studying how the use of quantum systems might enhance the performance of certain information processing tasks. The primary goal of this thesis is to shed light on the natures and interrelationships of these phenomena by approaching them from the point of view afforded by information theory. We attempt to better understand these pillars of quantum mechanics by studying the various ways in which they govern the manipulation of information, while at the same time gaining valuable insight into the roles they play in specific applications. The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems and yield vital insights into the design of protocols for the quantum control of ensembles with potential applications in the field of quantum computing. By augmenting the existing formalism for quantifying entangled correlations, we show how this entanglement sharing behavior may be studied in increasingly complex systems of both theoretical and experimental significance. Further, our results shed light on the dynamical generation and evolution of multipartite entanglement by demonstrating that individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. The findings presented in this thesis support the conjecture that Hilbert space dimension is an objective property of a quantum system since it constrains the number of valid conceptual divisions of the system into subsystems. These arbitrary observer-induced distinctions are integral to the theory since
Quantum gravity, dynamical phase-space and string theory
NASA Astrophysics Data System (ADS)
Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
2014-08-01
In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).
Self field electromagnetism and quantum phenomena
NASA Astrophysics Data System (ADS)
Schatten, Kenneth H.
1994-07-01
Quantum Electrodynamics (QED) has been extremely successful inits predictive capability for atomic phenomena. Thus the greatest hope for any alternative view is solely to mimic the predictive capability of quantum mechanics (QM), and perhaps its usefulness will lie in gaining a better understanding of microscopic phenomena. Many ?paradoxes? and problematic situations emerge in QED. To combat the QED problems, the field of Stochastics Electrodynamics (SE) emerged, wherein a random ?zero point radiation? is assumed to fill all of space in an attmept to explain quantum phenomena, without some of the paradoxical concerns. SE, however, has greater failings. One is that the electromagnetic field energy must be infinit eto work. We have examined a deterministic side branch of SE, ?self field? electrodynamics, which may overcome the probelms of SE. Self field electrodynamics (SFE) utilizes the chaotic nature of electromagnetic emissions, as charges lose energy near atomic dimensions, to try to understand and mimic quantum phenomena. These fields and charges can ?interact with themselves? in a non-linear fashion, and may thereby explain many quantum phenomena from a semi-classical viewpoint. Referred to as self fields, they have gone by other names in the literature: ?evanesccent radiation?, ?virtual photons?, and ?vacuum fluctuations?. Using self fields, we discuss the uncertainty principles, the Casimir effects, and the black-body radiation spectrum, diffraction and interference effects, Schrodinger's equation, Planck's constant, and the nature of the electron and how they might be understood in the present framework. No new theory could ever replace QED. The self field view (if correct) would, at best, only serve to provide some understanding of the processes by which strange quantum phenomena occur at the atomic level. We discuss possible areas where experiments might be employed to test SFE, and areas where future work may lie.
A New Theory of the Electromagnetic Field
NASA Astrophysics Data System (ADS)
Kriske, Richard
2017-01-01
This author has previously introduced a new theory of the Electromagnetic Field and its interaction with matter. There was from the start a problem with Einstein's formulation of Invariants and its use in describing The EM field. The photon produced by first varying a stationary Electric field in one observer's reference frame is not the same as a photon produced from varying the a stationary Magnetic Field. The Magnetic field photon is thought of as being ``off the mass shell''. The Quantum information seems to carry with it an ordering of these events. You see this ordering in Wick's theory and in Feynman diagrams. This author is proposing that other fields can vary first in another Observers reference frame, not just the ``Scalar Field'' or the ``Fermion Field'', but many other forms of Energy. If the ``Nuclear Field'' varies first, it results in Quantum information that produces a photon that has the Nuclear Field in it and also the Magnetic Field, this is the strange effect seen in Nuclear Magnetic Resonance. This author proposed that there is a large number of photons with different properties, because of this ordering of events that occurs in Quantum Information. One of these photons is the Neutrino which appears to be a three field photon. This is Kriske's Field Theory.