Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Generalized Gibbs ensembles for quantum field theories
NASA Astrophysics Data System (ADS)
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2015-05-01
We consider the nonequilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In the presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra)local in the usual sense of QFTs, but fulfill a significantly weaker form of locality. We discuss the implications of our results for integrable QFTs in one spatial dimension.
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.
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. PMID:22654052
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 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…
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.
Studies in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bastianelli, Fiorenzo
We analyze several topics in quantum field theory, mainly motivated by their role in the formulation of string theories. The common theme in what follows is the implementation of symmetries, such as local supersymmetry or BRST symmetry, through an action principle and the analysis of anomalies, the latter describing the breakdown of these symmetries at the quantum level. In the first part of this dissertation, we analyze "chiral bosons", i.e. massless scalar fields in a two -dimensional spacetime propagating in only one of the two light-cone directions. We present a general method for constructing couplings for chiral bosons and give details for the coupling to supergravity. The notion of a two dimensional chiral boson is generalized in d = 4k + 2 spacetime dimensions to that of a self-dual antisymmetric tensor field. We derive the coupling to gravity and compute the gravitational anomalies using the Feynman rules obtained from the action. We find agreement with the important work of Alvarez-Gaume and Witten, who conjectured the relevant Feynman rules. Our result therefore completes and justifies the Alvarez-Gaume-Witten findings. For the case of d = 2 we also show how to use the method of Fujikawa for computing anomalies from the non-invariance of the path integral measure. We obtain the full effective action by integrating the anomaly equation. In the second part we focus on a method for computing the consistent anomalies in the Fujikawa scheme. In a first application, we derive the consistent regulators for the various fields of the quantum action of the spinning string in superspace. These regulators produce the anomalies which satisfy the Wess-Zumino consistency conditions. In a second application, we analyze the anomalous structure of the Green-Schwarz formulation of the heterotic string. We find anomalies which generically do not cancel on an arbitrary world-sheet manifold. This raises questions concerning the possible validity of such a formulation of
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.
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).
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Supergeometry in Locally Covariant Quantum Field Theory
NASA Astrophysics Data System (ADS)
Hack, Thomas-Paul; Hanisch, Florian; Schenkel, Alexander
2016-03-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc to S* Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc to eS* Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.
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.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Random walk in generalized quantum theory
Martin, Xavier; O'Connor, Denjoe; Sorkin, Rafael D.
2005-01-15
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we 'quantize' the classical random walk by finding, subject to a certain condition of 'strong positivity', the most general Markovian, translationally invariant 'decoherence functional' with nearest neighbor transitions.
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.
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.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
A master functional for quantum field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-04-01
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional Γ does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=ln Z, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to so-called proper fields, which allows us to work without passing through Z, W or Γ. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-01
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.
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
* Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
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.
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
Field Theory of the Quantum Kicked Rotor
Altland, A.; Zirnbauer, M.R.
1996-11-01
The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wavelength physics of the system is precisely the supersymmetric nonlinear {sigma} model for quasi-one-dimensional metallic wires. This proves that the analogy between chaotic systems with dynamical localization and disordered metals can indeed be exact. The role of symmetries is discussed.
Quantum Gravity from the Point of View of Locally Covariant Quantum Field Theory
NASA Astrophysics Data System (ADS)
Brunetti, Romeo; Fredenhagen, Klaus; Rejzner, Katarzyna
2016-08-01
We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.
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.
Quantum field theories on manifolds with curved boundaries: Scalar fields
NASA Astrophysics Data System (ADS)
McAvity, D. M.; Osborn, H.
1993-04-01
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the Green function for second-order differential operators valid in the neighbourhood of the boundary and which is obtained from a corresponding expansion of the associated heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The first few leading terms in the expansion are sufficient to calculate all additional divergences present in a perturbative loop expansion as a consequence of the presence of the boundary. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an O( n) symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet orgeneralized Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the β-function vanishes are also derived. For a general scalar field theory, where the fieldsø attain specified values ϕ in the boundary, the local Schrödinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. The perturbative expansion for the wave functional is defined by expansion around the solution of the classical field equations satisfying the required boundary values and the counterterms necessary to derive a finite hamiltonian operator, which includes a functional Laplace operator on the fields ϕ, are
"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.
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 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 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.
Generalized metric formulation of double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Hull, Chris; Zwiebach, Barton
2010-08-01
The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.
Quantum field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-08-01
We consider K-mouflage models, which are K-essence theories coupled to matter. We analyze their quantum properties and in particular the quantum corrections to the classical Lagrangian. We setup the renormalization program for these models and show that, contrary to renormalizable field theories where renormalization by infinite counterterms can be performed in one step, K-mouflage theories involve a recursive construction whereby each set of counterterms introduces new divergent quantum contributions which in turn must be subtracted by new counterterms. This tower of counterterms can be in principle constructed step by step by recursion and allows one to calculate the finite renormalized action of the model. In particular, it can be checked that the classical action is not renormalized and that the finite corrections to the renormalized action contain only higher-derivative operators. We concentrate then on the regime where calculability is ensured, i.e., when the corrections to the classical action are negligible. We establish an operational criterion for classicality and show that this is satisfied in cosmological and astrophysical situations for (healthy) K-mouflage models which pass the solar system tests. These results rely on perturbation theory around a background and are only valid when the background configuration is quantum stable. We analyze the quantum stability of astrophysical and cosmological backgrounds and find that models that pass the solar system tests are quantum stable. We then consider the possible embedding of the K-mouflage models in an UV completion. We find that the healthy models which pass the solar system tests all violate the positivity constraint which would follow from the unitarity of the putative UV completion, implying that these healthy K-mouflage theories have no UV completion. We then analyze their behavior at high energy, and we find that the classicality criterion is satisfied in the vicinity of a high-energy collision
Duret, Q.
2010-10-15
Starting from Wigner's symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman's definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance.
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.
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.
Infinite-time average of local fields in an integrable quantum field theory after a quantum quench.
Mussardo, G
2013-09-01
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.
Group field theories for all loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Ryan, James P.; Thürigen, Johannes
2015-02-01
Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.
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.
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
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
2014-07-01
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.
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.
Spectral methods in quantum field theory and quantum cosmology
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus
2012-09-01
We review the application of the spectral zeta function to the one-loop properties of quantum field theories on manifolds with boundary, with emphasis on Euclidean quantum gravity and quantum cosmology. As was shown in the literature some time ago, the only boundary conditions that are completely invariant under infinitesimal diffeomorphisms on metric perturbations suffer from a drawback, i.e. lack of strong ellipticity of the resulting boundary-value problem. Nevertheless, at least on the Euclidean 4-ball background, it remains possible to evaluate the ζ(0) value, which describes in this case a universe which, in the limit of small 3-geometry, has vanishing probability of approaching the cosmological singularity. An assessment of this result is performed here, discussing its physical and mathematical implications. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
The quantum field theory of electric and magnetic charge
NASA Astrophysics Data System (ADS)
Blagojević, M.; Senjanović, P.
1988-01-01
The dynamics of monopoles as quantum objects is described by the quantum field theory of monopoles and charges. Owing to the presence of a preferred direction n, this is the first example of a theory which is not manifestly Lorentz invariant, though intrinsically it possesses this invariance. Another unusual property of this Abelian theory is that it has two coupling constants connected via the quatization condition. The investigation of the basic properties of the theory is facilitated by the existence of various formulations. Thus, Lorentz invariance, which is not easily seen in Schwinger's Hamiltonian framework, is transparent after the introduction of the particle-path representation of Zwanziger's local Langrarian formulation. Ultraviolet properties of the theory receive a superior, n-independent treatment in this representation, with the result that favors opposite renormalization of electric and magnetic charge. The physical content of infrared regularization is clearly described in the one-potential formulation. Several other topics are treated: Dirac's quantum mechanics of the monopole, connection with non-Abelian monopoles, a supersymmetric generalization of the theory, and its possible role in preon dynamics.
Christensen, S.M.
1984-01-01
The book of essay entitled Quantum Theory of Gravity, edited by Steven M. Christensen is reviewed. The book contains over thirty papers dealing with the subject of the unification of quantum field theory and general relativity theory. Contributions include discussions of non-Abelian gauge theories, supersymmetry, issues in renormalization and quantization and matters related to the interpretation of theories.
Pfalzgraff, William C; Kelly, Aaron; Markland, Thomas E
2015-12-01
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.
Reconstruction in quantum field theory with a fundamental length
Soloviev, M. A.
2010-09-15
In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex l-neighborhood of the real space and are localizable at scales large compared to l. The causality condition is formulated as continuity of the field commutator in an appropriate topology associated with the light cone. We prove that the relevant function spaces are nuclear and derive the kernel theorems for the corresponding classes of multilinear functionals, which provides the basis for the reconstruction procedure. Special attention is given to the accurate determination of the domain of the reconstructed quantum fields in the Hilbert space of states. We show that the primitive common invariant domain must be suitably extended to implement the (quasi)localizability and causality conditions.
Quantum κ-deformed differential geometry and field theory
NASA Astrophysics Data System (ADS)
Mercati, Flavio
2016-03-01
I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.
No resonant tunneling in standard scalar quantum field theory
NASA Astrophysics Data System (ADS)
Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.
2008-01-01
We investigate the nature of resonant tunneling in standard scalar Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu we describe the quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path'' (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.
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.
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.
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.
Jets and Metastability in Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Farhi, David
I give a high level overview of the state of particle physics in the introduction, accessible without any background in the field. I discuss improvements of theoretical and statistical methods used for collider physics. These include telescoping jets, a statistical method which was claimed to allow jet searches to increase their sensitivity by considering several interpretations of each event. We find that indeed multiple interpretations extend the power of searches, for both simple counting experiments and powerful multivariate fitting experiments, at least for h → bb¯ at the LHC. Then I propose a method for automation of background calculations using SCET by appropriating the technology of Monte Carlo generators such as MadGraph. In the third chapter I change gears and discuss the future of the universe. It has long been known that our pocket of the standard model is unstable; there is a lower-energy configuration in a remote part of the configuration space, to which our universe will, eventually, decay. While the timescales involved are on the order of 10400 years (depending on how exactly one counts) and thus of no immediate worry, I discuss the shortcomings of the standard methods and propose a more physically motivated derivation for the decay rate. I then make various observations about the structure of decays in quantum field theory.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
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 constrains traversable wormhole geometries
Ford, L.H. |; Roman, T.A. |
1996-05-01
Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
Quantum Field Theory in Coordinate Space
NASA Astrophysics Data System (ADS)
Erdogan, Ahmet Ozan
In order to provide a new coordinate-space perspective applicable to scattering amplitudes, in the first part of this dissertation, the structure of singularities in perturbative massless gauge theories is investigated in coordinate space. The pinch singularities in coordinate-space integrals occur at configurations of vertices which have a direct interpretation in terms of physical scattering of particles in real space-time in the same way as for the loop momenta in the case of momentum-space singularities. In the analysis of vertex functions in coordinate space, the well-known factorization into hard, soft, and jet functions is found. By power-counting arguments, it is found that coordinate-space integrals of vertex functions have logarithmic divergences at worst. The `hard-collinear' and `soft-collinear' approximations that allow the application of gauge theory Ward identities in the formal proof of factorization in coordinate space are introduced. In the second part, the perturbative cusp and closed polygons of Wilson lines for massless gauge theories are analyzed in coordinate space, and expressed as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link renormalization scales with invariant distances. A direct perturbative prescription for the logarithm of the cusp and related cross sections treated in eikonal approximation is provided by web diagrams. The sources of their ultraviolet poles in coordinate space associated with their nonlocal collinear divergences are identified by the power-counting technique explained in the first part. In the study of the coordinate-space matrix elements that correspond to scattering amplitudes involving partons and Wilson lines in coordinate space, a series of subtractions is developed to eliminate their divergences and to show their factorization in coordinate space. The ultraviolet finiteness of the web integrand is shown by relating the web expansion to the application of
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Fodor, Z.; Hoelbling, C.; Katz, S. D.; Lellouch, L.; Portelli, A.; Szabo, K. K.; Toth, B. C.
2016-04-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
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.
Continuum regularization of quantum field theory
Bern, Z.
1986-01-01
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, difficulties arise which, in general, ruins the scheme. 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.
Gravity Dual for Reggeon Field Theory and Nonlinear Quantum Finance
NASA Astrophysics Data System (ADS)
Nakayama, Yu
We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-01
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 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.
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 Field Theory and Gravity: Black Holes and Dark Matter
NASA Astrophysics Data System (ADS)
Heo, Junseong
1998-11-01
This thesis examines the various field theory related issues motivated by the gravitational phenomena. Black Holes with quantum degrees of freedom, non-abelian generalization of vortex solutions, and WIMP detection rates for the ongoing experimental search for dark matter are explored. We derive a close relation between the Minkowski signature approach and the Euclidean formalism in the construction of quantum degrees of freedom on a Black hole solution. We demonstrate the benefit of a physically transparent energy momentum consideration and extend the previous analysis on Hawking temperature shifts. Specifically we clear up the issue of thick string limit behavior that obscures the direct intuition and draw an analogy that brings the instanton solutions in flat two dimensional planes to Euclidean vortex solutions in the black hole background. These considerations lead to the question on the various possibilities of non-abelian solutions which supply the seed for the source of quantum hair in general context. We construct an explicit non-abelian vortex solution with a remnant Z3 discrete symmetry and consider its new interaction properties distinct from the known abelian solution behavior. Dark Matter direct search experiments are now in operation yet the expected event rate is very low and the previously available theoretical formalism could not tell the differences among different halo models. We present a derivation of angle dependent differential event rates which allows this possibility, and enables the confirmation of detection of a galactic halo WIMP signal with a smaller number of experimental signals. It may open up realistic methods to distinguish one halo model from another.
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
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
Universal scaling in fast quantum quenches in conformal field theories.
Das, Sumit R; Galante, Damián A; Myers, Robert C
2014-05-01
We study the time evolution of a conformal field theory deformed by a relevant operator under a smooth but fast quantum quench which brings it to the conformal point. We argue that when the quench time scale δt is small compared to the scale set by the relevant coupling, the expectation value of the quenched operator scales universally as δλ/δt(2Δ-d), where δλ is the quench amplitude. This growth is further enhanced by a logarithmic factor in even dimensions. We present explicit results for free scalar and fermionic field theories, supported by an analytic understanding of the leading contribution for fast quenches. Our results suggest that this scaling result, first found in holography, is in fact quite general. Our considerations also show that this limit of fast smooth quenches is quite different from an instantaneous quench from one time-independent Hamiltonian to another, where the state at the time of the quench serves as an initial condition for subsequent evolution with the final Hamiltonian.
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.
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.
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.
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.
Wigner's inequalities in quantum field theory
Nikitin, Nikolai; Toms, Konstantin
2010-09-15
We present a relativistic generalization of the Wigner inequality for the scalar and pseudoscalar particles decaying to two particles with spin (fermions and photons.) We consider Wigner's inequality with the full spin anticorrelation (with the nonrelativistic analog), as well as the case with the full spin correlation. The latter case may be obtained by a special choice of the plane of measurement of the spin projections on the direction of propagation of fermions. The possibility for relativistic testing of Bohr's complementarity principle is shown.
Spin operator and entanglement in quantum field theory
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo; Oh, C. H.; Zhang, Chengjie
2014-07-01
Entanglement is studied in the framework of Dyson's S-matrix theory in relativistic quantum field theory, which leads to a natural definition of entangled states of a particle-antiparticle pair and the spin operator from a Noether current. As an explicit example, the decay of a massive pseudo-scalar particle into a pair of electron and positron is analyzed. Two spin operators are extracted from the Noether current. The Wigner spin operator characterizes spin states at the rest frame of each fermion and, although not measurable in the laboratory, gives rise to a straightforward generalization of low-energy analysis of entanglement to the ultrarelativistic domain. In contrast, if one adopts a (modified) Dirac spin operator, the entanglement measured by spin correlation becomes maximal near the threshold of the decay, while the entanglement is replaced by the classical correlation for the ultrarelativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables type of description is possible. Chiral symmetry differentiates the spin angular momentum and the magnetic moment. The use of weak interaction that can measure helicity is suggested in the analysis of entanglement at high energies instead of a Stern-Gerlach apparatus, which is useless for the electron. A difference between the electron spin at high energies and the photon linear polarization is also noted. The Standard Model can describe all of the observable properties of leptons.
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
Quantum hair, magnetic monopoles and topology in quantum field theory
NASA Astrophysics Data System (ADS)
Liu, Hong
This dissertation is divided into two parts: In the first part, we present results obtained by a consideration of the non-classical energy momentum tensor associated with Euclidean Instantons outside the event horizon of black holes. We demonstrate how this allows an analytic estimate to be made of the effect of discrete quantum hair on the temperature of the black hole, in which the role of violations of the weak energy condition associated with instantons is made explicit, and in which the previous results are extended. Last, we demonstrate how the existence of a non-classical electric field outside the event horizon of black holes can be identified with a well-known effect in the Abelian-Higgs model in two dimensions. In this case, there is a one-to- one connection between the discrete charge of a black hole and a topological phase in two dimensions. In the second part, we find the spectrum of magnetic monopoles produced in the symmetry breaking SU(5) /to Glow = [ SU(3) × SU(2) × U(1)']/Z6 by constructing classical bound states of the fundamental monopoles. The spectrum of monopoles is found to correspond to the spectrum of one family of standard model fermions and hence, is a starting point for constructing the dual standard model. If the SU(3) factor now breaks down to Z3, the monopoles with non-trivial SU(3) charge get confined by strings in SU(3) singlets. We then discuss the fate of the monopoles if the [ SU(2) × U(1)']'Z2 factor breaks down to U(1)Q by a Higgs mechanism as in the electroweak model. Last, a more elaborate model is constructed to address the family replication problem. The breaking of a simple grand unified group to [ Glow × H1 × H2 × H3]/Z53 and then further to Glow, produces three families of stable monopoles each of whose magnetic quantum numbers correspond to the electric charges on the fermions of the Standard Model. Here Hi are simple Lie groups which each have a Z5 symmetry in common with Glow.
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.
Horava—Lifshitz Type Quantum Field Theory and Hierarchy Problem
NASA Astrophysics Data System (ADS)
Wei, Chao
2016-06-01
We study the Lifshitz type extension of the standard model (SM) at the UV, with dynamical critical exponent z = 3. One loop radiative corrections to the Higgs mass in such a model are calculated. Our result shows that, the Hierarchy problem, which has initiated many excellent extension of the minimal SM, may be weakened in the z = 3 Lifshitz type quantum field theory. Supported by the National Natural Science Foundation of China
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.
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.
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
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.
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. PMID:27482736
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.
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.
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.
New method for calculating binding energies in quantum mechanics and quantum field theories
Gat, G.; Rosenstein, B. Institute of Physics, Academia Sinica, Taipei, 11529 )
1993-01-04
We propose a systematic perturbative method for calculating the binding energy of threshold bound states---states which exist for arbitrary small coupling. The starting point is a (regularized) free theory. Explicit calculations are performed for quantum mechanics with arbitrary short-range potential in 1D and various (1+1)-dimensional quantum field theories. We check the method by comparing the results with exact formulas available in solvable models.
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.
An Algebraic Construction of Boundary Quantum Field Theory
NASA Astrophysics Data System (ADS)
Longo, Roberto; Witten, Edward
2011-04-01
We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras {mathcal A_V} on the Minkowski half-plane M + starting with a local conformal net {mathcal A} of von Neumann algebras on {mathbb R} and an element V of a unitary semigroup {mathcal E(mathcal A)} associated with {mathcal A}. The case V = 1 reduces to the net {mathcal A_+} considered by Rehren and one of the authors; if the vacuum character of {mathcal A} is summable, {mathcal A_V} is locally isomorphic to {mathcal A_+}. We discuss the structure of the semigroup {mathcal E(mathcal A)}. By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to {mathcal E(mathcal A^{(0)})} with {mathcal A^{(0)}} the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mack-Todorov extension of {mathcal A^{(0)}}. A further family of models comes from the Ising model.
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. PMID:27091160
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.
Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
NASA Astrophysics Data System (ADS)
Kita, T.
2010-04-01
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keld ysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Phi-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Phi-derivable approximation, i.e., an issue of how to handle the ``Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy''. Aim (ii) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems ca n be handled
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Ocampo, Hernan; Pariguan, Eddy; Paycha, Sylvie
2010-04-01
Introduction; 1. The impact of QFT on low-dimensional topology Paul Kirk; 2. Differential equations aspects of quantum cohomology Martin A. Guest; 3. Index theory and groupoids Claire Debord and Jean-Marie Lescure; 4. Renormalization Hopf algebras and combinatorial groups Alessandra Frabetti; 5. BRS invariance for massive boson fields José M. Gracia-Bondía; 6. Large N field theories and geometry David Berenstein; 7. Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity Martin Reuter and Frank Saueressig; 8. When is a differentiable manifold the boundary of an orbifold? Andrés Angel; 9. Canonical group quantization, rotation generators and quantum indistinguishability Carlos Benavides and Andrés Reyes-Lega; 10. Conserved currents in Kähler manifolds Jaime R. Camacaro and Juan Carlos Moreno; 11. A symmetrized canonical determinant on odd-class pseudodifferential operators Marie-Françoise Ouedraogo; 12. Some remarks about cosymplectic metrics on maximal flag manifolds Marlio Paredes and Sofia Pinzón; 13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures Jorge Plazas; Index.
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.
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.
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.
Quantum field theory of van der Waals friction
Volokitin, A. I.; Persson, B. N. J.
2006-11-15
van der Waals friction between two semi-infinite solids, and between a small neutral particle and semi-infinite solid is studied using thermal quantum field theory in the Matsubara formulation. We show that the friction to linear order in the sliding velocity can be obtained from the equilibrium Green functions and that our treatment can be extended for bodies with complex geometry. The calculated friction agrees with the friction obtained using a dynamical modification of the Lifshitz theory, which is based on the fluctuation-dissipation theorem. We show that it should be possible to measure the van der Waals friction in noncontact friction experiment using state-of-the-art equipment.
Generalized Lee-Wick formulation from higher derivative field theories
Cho, Inyong; Kwon, O-Kab
2010-07-15
We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.
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 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.
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.
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2016-01-01
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum gravity theory. The gravifield sided on both locally flat noncoordinate spacetime and globally flat Minkowski spacetime is an essential ingredient for gauging global spin and scaling symmetries. The locally flat gravifield spacetime spanned by the gravifield is associated with a noncommutative geometry characterized by a gauge-type field strength of the gravifield. A coordinate-independent and gauge-invariant action for the quantum gravity is built in the gravifield basis. In the coordinate basis, we derive equations of motion for all quantum fields including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for the gravifield tensor is deduced in connection directly with the total energy-momentum tensor. When the spin and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we obtain exact solutions by solving equations of motion for the background fields in a unitary basis. The massless graviton and massive spinon result as physical quantum degrees of freedom. The resulting Lorentz-invariant and conformally flat background gravifield spacetime is characterized by a cosmic vector with a nonzero cosmological mass scale. The evolving Universe is, in general, not isotropic in terms of conformal proper time. The conformal size of the Universe becomes singular at the cosmological horizon and turns out to be inflationary in light of cosmic proper time. A mechanism for quantum scalinon inflation is demonstrated such that it is the quantum effect that causes the breaking of global scaling symmetry and generates the inflation of the early Universe, which is ended when the evolving vacuum expectation value of the
(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.
Interacting scalar field theory in general curved space-time
Kodaira, J.
1986-05-15
The ultraviolet divergences of two-loop diagrams in general curved space-time are determined for the six-dimensional phi/sup 3/ theory. The background-field method is used to evaluate the effective action. In order to isolate the short-distance singularities, the Feynman propagator is expanded by the heat kernel and dimensional regularization is employed. The gravitational counterterms as well as those for the matter field are explicitly given to the two-loop order.
Inequivalence of quantum field theories on noncommutative spacetimes: Moyal versus Wick-Voros planes
Balachandran, A. P.; Ibort, A.; Marmo, G.; Martone, M.
2010-04-15
In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can fail on the quantum field theory side. In particular, quantum field theory on the Wick-Voros and Moyal planes are shown to be inequivalent in a few different ways. Thus quantum field theory calculations on these planes will lead to different physics even though the classical theories are equivalent. This result is reminiscent of chiral anomaly in gauge theories and has obvious physical consequences. The construction of quantum field theories on the Wick-Voros plane has new features not encountered for quantum field theories on the Moyal plane. In fact it seems impossible to construct a quantum field theory on the Wick-Voros plane which satisfies all the properties needed of field theories on noncommutative spaces. The Moyal twist seems to have unique features which make it a preferred choice for the construction of a quantum field theory on a noncommutative spacetime.
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.
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.
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.
Neutral current neutrino oscillation via quantum field theory approach
NASA Astrophysics Data System (ADS)
Ettefaghi, M. M.; Askaripour Ravari, Z.
2015-07-01
Neutrino and anti-neutrino states coming from the neutral current or Z0 decay are blind with respect to the flavor. The neutrino oscillation is observed and formulated when its flavor is known. However, it has been shown that we can see neutrino oscillation pattern for Z0 decay neutrinos provided that both neutrino and anti-neutrino are detected. In this paper, we restudy this oscillation via quantum field theory approach. Through this approach, we find that the oscillation pattern ceases if the distance between the detectors is larger than the coherence length, while both neutrino and antineutrino states may be coherent. Also the uncertainty of source (region of Z0 decay) does not have any role in the coherency of neutrino and antineutrino.
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.
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 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.
Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?
NASA Astrophysics Data System (ADS)
Addazi, Andrea; Esposito, Giampiero
2015-05-01
The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality is expected to reappear at one loop. We suggest that the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e. by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory. An infinite number of divergent diagrams cancel each other by virtue of the nonrenormalization theorem of supersymmetry. However, supersymmetry is not enough to protect a theory from all acausal divergences. For instance, acausal contributions to supersymmetric corrections to D-terms are not protected by supersymmetry. On the other hand, we show in detail how supersymmetry also helps in dealing with D-terms: divergences are not canceled but they become softer than in the nonsupersymmetric case. The supergraphs' formalism turns out to be a powerful tool to reduce the complexity of perturbative calculations.
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.
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.
Towards Noncommutative Topological Quantum Field Theory - Hodge theory for cyclic cohomology
NASA Astrophysics Data System (ADS)
Zois, I. P.
2014-03-01
Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation.
No-go theorems for generalized chameleon field theories.
Wang, Junpu; Hui, Lam; Khoury, Justin
2012-12-14
The chameleon, or generalizations thereof, is a light scalar that couples to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: (i) the Compton wavelength of such a scalar can be at most ~/= 1 MPc at the present cosmic density, which restricts its impact to nonlinear scales; and (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time, which precludes the possibility of self-acceleration. These results imply that chameleonlike scalar fields have a negligible effect on the linear-scale growth history; theories that invoke a chameleonlike scalar to explain cosmic acceleration rely on a form of dark energy rather than a genuine modified gravity effect. Our analysis applies to a broad class of chameleon, symmetron, and dilaton theories. PMID:23368302
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
2011-03-01
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.
Quantum Field Theories on the Lattice : Concepts behind their Numerical Simulations
NASA Astrophysics Data System (ADS)
Bietenholz, Wolfgang
2011-09-01
We review the basic ideas behind numerical simulations of quantum field theory, which lead to non-perturbative results in particle physics. We first sketch the functional integral formulation of quantum mechanics, its transition to Euclidean time and the link to statistical mechanics. Then we proceed to quantum field theory in the lattice regularization, and its applications to scalar fields, gauge fields and fermions. In particular we address the treatment of chiral symmetry. At last we describe the formulation of lattice QCD and comment on simulations and results.
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.
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.
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.
On estimating perturbative coefficients in quantum field theory and statistical physics
Samuel, M.A. |
1994-05-01
The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent.
Quantum correlated cluster mean-field theory applied to the transverse Ising model
NASA Astrophysics Data System (ADS)
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.
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.
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. PMID:27415217
NASA Astrophysics Data System (ADS)
Barral, David; Liñares, Jesús; Nistal, María C.
2013-07-01
A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger's cat states is analyzed.
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
Simple space-time symmetries: Generalizing conformal field theory
Mack, Gerhard; Riese, Mathias de
2007-05-15
We study simple space-time symmetry groups G which act on a space-time manifold M=G/H which admits a G-invariant global causal structure. We classify pairs (G,M) which share the following additional properties of conformal field theory. (1) The stability subgroup H of o set-membership sign M is the identity component of a parabolic subgroup of G, implying factorization H=MAN{sup -}, where M generalizes Lorentz transformations, A dilatations, and N{sup -} special conformal transformations. (2) Special conformal transformations {xi} set-membership sign N{sup -} act trivially on tangent vectors v set-membership sign T{sub o}M. The allowed simple Lie groups G are the universal coverings of SU(m,m),SO(2,D),Sp(l,R),SO*(4n), and E{sub 7(-25)} and H are particular maximal parabolic subgroups. They coincide with the groups of fractional linear transformations of Euclidean Jordan algebras whose use as generalizations of Minkowski space-time was advocated by Guenaydin [Mod. Phys. Lett. A 8, 1407 (1993)]. All these groups G admit positive energy representations. It will also be shown that the classical conformal groups SO(2,D) are the only allowed groups which possess an automorphism with properties appropriate for a time reflection.
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.
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…
Walach, H
2003-08-01
Homeopathy is scientifically banned, both for lack of consistent empirical findings, but more so for lack of a sound theoretical model to explain its purported effects. This paper makes an attempt to introduce an explanatory idea based on a generalized version of quantum mechanics (QM), the weak quantum theory (WQT). WQT uses the algebraic formalism of QM proper, but drops some restrictions and definitions typical for QM. This results in a general axiomatic framework similar to QM, but more generalized and applicable to all possible systems. Most notably, WQT predicts entanglement, which in QM is known as Einstein-Podolsky-Rosen (EPR) correlatedness within quantum systems. According to WQT, this entanglement is not only tied to quantum systems, but is to be expected whenever a global and a local variable describing a system are complementary. This idea is used here to reconstruct homeopathy as an exemplification of generalized entanglement as predicted by WQT. It transpires that homeopathy uses two instances of generalized entanglement: one between the remedy and the original substance (potentiation principle) and one between the individual symptoms of a patient and the general symptoms of a remedy picture (similarity principle). By bringing these two elements together, double entanglement ensues, which is reminiscent of cryptographic and teleportation applications of entanglement in QM proper. Homeopathy could be a macroscopic analogue to quantum teleportation. This model is exemplified and some predictions are derived, which make it possible to test the model. PMID:12972724
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.
NASA Astrophysics Data System (ADS)
Johnson, David T.
Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in
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. PMID:25763944
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.
Nonequilibrium GREEN’S Functions for High-Field Quantum Transport Theory
NASA Astrophysics Data System (ADS)
Bertoncini, Rita
A formulation of the Kadanoff-Baym-Keldysh theory of nonequilibrium quantum statistical mechanics is developed in order to describe nonperturbatively the effects of the electric field on electron-phonon scattering in nondegenerate semiconductors. We derive an analytic, gauge-invariant model for the spectral density of energy states that accounts for both intracollisional field effect and collisional broadening simultaneously. A kinetic equation for the quantum distribution function is derived and solved numerically. The nonlinear drift velocity versus applied field characteristics is also evaluated numerically. Many features of our nonlinear theory bear formal resemblance to linear-response theory.
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
Equivalence of quantum field theories related by the θ -exact Seiberg-Witten map
NASA Astrophysics Data System (ADS)
Martin, Carmelo P.; Trampetić, Josip; You, Jiangyang
2016-08-01
The equivalence of the noncommutative U(N) quantum field theories related by the θ -exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N =0 , 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N =0 , 1, 2, 4 supersymmetry.
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.
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.
The geometrical structure of quantum theory as a natural generalization of information geometry
Reginatto, Marcel
2015-01-13
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
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.
Effective field theory and projective construction for Zk parafermion fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2010-04-01
The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the simpler integer quantum Hall states. Here we show how to apply the projective construction to the Zk parafermion (Laughlin/Moore-Read/Read-Rezayi) FQH states, which occur at filling fraction ν=k/(kM+2) . This allows us to derive the bulk low-energy effective field theory for these topological phases, which is found to be a Chern-Simons theory at level 1 with a U(M)×Sp(2k) gauge field. This approach also helps us understand the non-Abelian quasiholes in terms of holes of the integer quantum Hall states.
Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems
NASA Astrophysics Data System (ADS)
Marino, Jamir; Diehl, Sebastian
2016-08-01
We develop a quantum dynamical field theory for studying phase transitions in driven open systems coupled to Markovian noise, where nonlinear noise effects and fluctuations beyond semiclassical approximations influence the critical behavior. We systematically compare the diagrammatics, the properties of the renormalization group flow, and the structure of the fixed points of the quantum dynamical field theory and of its semiclassical counterpart, which is employed to characterize dynamical criticality in three-dimensional driven-dissipative condensates. As an application, we perform the Keldysh functional renormalization of a one-dimensional driven open Bose gas, where a tailored diffusion Markov noise realizes an analog of quantum criticality for driven-dissipative condensation. We find that the associated nonequilibrium quantum phase transition does not map into the critical behavior of its three-dimensional classical driven counterpart.
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2003-06-01
I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary spacetime dimensions. I prove that when the spacetime manifold admits a metric of constant curvature, the propagator is not affected by terms with higher derivatives. More generally, certain Lagrangian terms are not turned on by renormalization, if they are absent at the tree level. This restricts the form of the action of a non-renormalizable theory, and has applications to quantum gravity. The new action contains infinitely many couplings, but not all of the ones that might have been expected. In quantum gravity, the metric of constant curvature is an extremal, but not a minimum, of the complete action. Nonetheless, it appears to be the right perturbative vacuum, at least when the curvature is negative, suggesting that the quantum vacuum has a negative asymptotically constant curvature. The results of this paper give also a set of rules for a more economical use of effective quantum field theories and suggest that it might be possible to give mathematical sense to theories with infinitely many couplings at high energies, to search for physical predictions.
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.
Moving Beyond Quantum Mechanics in Search for a Generalized Theory of Superconductivity
NASA Astrophysics Data System (ADS)
Akpojotor, Godfrey; Animalu, Alexander
2012-02-01
Though there are infinite number of theories currently in the literature in the search for a generalized theory of superconductivity (SC), there may be three domineering mechanisms for the Cooper pair formation (CPF) and their emergent theories of SC. Two of these mechanisms, electron-phonon interactions and electron-electron correlations which are based on the quantum theory axiom of action-at-a distance, may be only an approximation of the third mechanism which is contact interaction of the wavepackets of the two electrons forming the Cooper pair as envisaged in hadronic mechanics to be responsible for natural bonding of elements. The application of this hydronic --type interaction to the superconducting cuprates, iron based compounds and heavy fermions leads to interesting results. It is therefore suggested that the future of the search for the theory of SC may be considered from this natural possible bonding that at short distances, the CPF is by a nonlinear, nonlocal and nonhamiltonian strong hadronic-type interactions due to deep wave-overlapping of spinning particles leading to Hulthen potential that is attractive between two electrons in singlet couplings while at large distances the CPF is by superexchange interaction which is purely a quantum mechanical affairs.
NASA Astrophysics Data System (ADS)
Hofer-Szabó, Gábor; Vecsernyés, Péter
2012-02-01
In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones {mathcal{O}}a and {mathcal{O}}b, respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of {mathcal{O}}a and {mathcal{O}}b and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models.
NASA Astrophysics Data System (ADS)
Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
2016-05-01
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding end points, and proceed by identifying classical (minimal Euclidean action) path, to be referred to as a flucton, which passes through this end point. Fluctuations around a flucton path are included, by standard Feynman diagrams, previously developed for instantons. We calculate the Green function and evaluate the one loop determinant both by direct diagonalization of the fluctuation equation and also via the trick with the Green functions. The two-loop corrections are evaluated by explicit Feynman diagrams, and some curious cancellation of logarithmic and polylog terms is observed. The results are fully consistent with large-distance asymptotics obtained in quantum mechanics. Two classic examples—quartic double-well and sine-Gordon potentials—are discussed in detail, while powerlike potential and quartic anharmonic oscillator are discussed in brief. Unlike other semiclassical methods, like WKB, we do not use the Schrödinger equation, and all the steps generalize to multidimensional or quantum fields cases straightforwardly.
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.
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.
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.
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.
Sindelka, Milan; Moiseyev, Nimrod
2006-04-27
We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications, such as alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational, and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac-field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian.
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.
Time Machines and Quantum Theory
NASA Astrophysics Data System (ADS)
Hadley, Mark J.
2008-09-01
There is a deep structural link between acausal spacetimes and quantum theory. As a consequence quantum theory may resolve some "paradoxes" of time travel. Conversely, non-time-orientable spacetimes naturally give rise to electric charges and spin half. If an explanation of quantum theory is possible, then general relativity with time travel could it.
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.
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.
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.
Quantum field theory of photon–Dirac fermion interacting system in graphene monolayer
NASA Astrophysics Data System (ADS)
Nguyen, Bich Ha; Hieu Nguyen, Van
2016-06-01
The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields.
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
On a derivation of the Boltzmann equation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Leiler, Gregor
The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.
NASA Astrophysics Data System (ADS)
Dolby, Carl E.; Gull, Stephen F.
2001-11-01
A reformulation of fermionic QFT in electromagnetic backgrounds is presented which uses methods analogous to those of conventional multiparticle quantum mechanics. Emphasis is placed on the (Schrödinger picture) states of the system, described in terms of Slater determinants of Dirac states, and not on the field operator ψ̂(x) (which is superfluous in this approach). The vacuum state "at time τ" is defined as the Slater determinant of a basis for the span of the negative spectrum of the "first quantized" Hamiltonian H(τ), thus providing a concrete realisation of the Dirac Sea. The general S-matrix element of the theory is derived in terms of time-dependent Bogoliubov coefficients, demonstrating that the S-matrix follows directly from the definition of inner product between Slater determinants. The process of "Hermitian extension," inherited directly from conventional multiparticle quantum mechanics, allows second quantized operators to be defined without appealing to a complete set of orthonormal modes and provides an extremely straightforward derivation of the general expectation value of the theory. The concept of "radar time," advocated by Bondi in his work on k-calculus, is used to generalise the particle interpretation to an arbitrarily moving observer. A definition of particle results, which depends only on the observer's motion and the background present, not on any choice of coordinates or gauge, or of the particle detector. We relate this approach to conventional methods by comparing and contrasting various derivations. Our particle definition can be viewed as a generalisation to arbitrary observers of the approach of G. W. Gibbons (1975, Comm. Math. Phys.44, 245).
How to take particle physics seriously: A further defence of axiomatic quantum field theory
NASA Astrophysics Data System (ADS)
Fraser, Doreen
Further arguments are offered in defence of the position that the variant of quantum field theory (QFT) that should be subject to interpretation and foundational analysis is axiomatic quantum field theory. I argue that the successful application of renormalization group (RG) methods within alternative formulations of QFT illuminates the empirical content of QFT, but not the theoretical content. RG methods corroborate the point of view that QFT is a case of the underdetermination of theory by empirical evidence. I also urge caution in extrapolating interpretive conclusions about QFT from the application of RG methods in other contexts (e.g., condensed matter physics). This paper replies to criticisms advanced by David Wallace, but aims to be self-contained.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Thermalization and revivals after a quantum quench in conformal field theory.
Cardy, John
2014-06-01
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
Thermalization and revivals after a quantum quench in conformal field theory.
Cardy, John
2014-06-01
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
Domain walls, fusion rules, and conformal field theory in the quantum Hall regime.
Ardonne, Eddy
2009-05-01
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.
Towards Noncommutative Topological Quantum Field Theory: Tangential Hodge-Witten cohomology
NASA Astrophysics Data System (ADS)
Zois, I. P.
2014-03-01
Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian.
Functional integral equation for the complete effective action in quantum field theory
NASA Astrophysics Data System (ADS)
Scharnhorst, K.
1997-02-01
Based on a methodological analysis of the effective action approach, certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral formulation of Lagrangian quantum field theory, we propose a functional integral equation for the complete effective action which can be understood as a certain fixed-point condition. This is motivated by a critical attitude toward the distinction, artificial from an experimental point of view, between classical and effective action. While for free field theories nothing new is accomplished, for interacting theories the concept differs from the established paradigm. The analysis of this new concept concentrates on gauge field theories, treating QED as the prototype model. An approximative approach to the functional integral equation for the complete effective action of QED is exploited to obtain certain nonperturbative information about the quadratic kernels of the action. As a particular application the approximate calculation of the QED coupling constant α is explicitly studied. It is understood as one of the characteristics of a fixed point given as a solution of the functional integral equation proposed. Finally, within the present approach the vacuum energy problem is considered, as are possible implications for the concept of induced gravity.
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
The theorem of Greenberg and Robinson for two-dimensional quantum field theories
NASA Astrophysics Data System (ADS)
Baumann, Klaus
1989-10-01
In two space-time dimensions there are quantum fields φ obeying ⧠φ=0, which nevertheless have nonvanishing higher truncated n-point functions. Such fields show up if one wants to adapt the theorem of Greenberg and Robinson to 1+1 space-time dimensions. Using the Jost-Lehmann-Dyson representation we show that if either (a) φ˜(p)=0 for spacelike momenta or (b) W˜φ+φ(p) decreases at least like exp(-p2), then the field φ is the sum of two local fields A and B, where A is a generalized free field and B satisfies ⧠B=0.
Unifying the Geometry of General Relativity with the Virtual Particle Nature of Quantum Theory
NASA Astrophysics Data System (ADS)
Laubenstein, John
2007-03-01
General Relativity (GR) and Quantum Electro-Dynamics (QED) utilize different underlying assumptions regarding the nature of vacuum and space-time. GR requires the actual geometry of space-time to change in the presence of mass resulting in gravitation. QED operates within flat space-time and propagates forces through the exchange of virtual photons. Efforts to unify these theories are -- despite their mathematical elegance -- complex, cumbersome and incomplete. The inability to achieve unification may suggest a need to re-think basic conceptual models. The IWPD Research Center has found evidence suggesting that time -- as a unique degree of freedom -- may be illusionary. Our research suggests that time may be ``embedded'' within a spatial dimension through a geometric manipulation of the light cone in Minkowski space-time. This interpretation of space-time provides predictions that are experimentally verifiable and suggests a conceptual path for the unification of GR and QED.
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.
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.
NASA Astrophysics Data System (ADS)
Yan, Jiawei; Ke, Youqi
2016-07-01
Electron transport properties of nanoelectronics can be significantly influenced by the inevitable and randomly distributed impurities/defects. For theoretical simulation of disordered nanoscale electronics, one is interested in both the configurationally averaged transport property and its statistical fluctuation that tells device-to-device variability induced by disorder. However, due to the lack of an effective method to do disorder averaging under the nonequilibrium condition, the important effects of disorders on electron transport remain largely unexplored or poorly understood. In this work, we report a general formalism of Green's function based nonequilibrium effective medium theory to calculate the disordered nanoelectronics. In this method, based on a generalized coherent potential approximation for the Keldysh nonequilibrium Green's function, we developed a generalized nonequilibrium vertex correction method to calculate the average of a two-Keldysh-Green's-function correlator. We obtain nine nonequilibrium vertex correction terms, as a complete family, to express the average of any two-Green's-function correlator and find they can be solved by a set of linear equations. As an important result, the averaged nonequilibrium density matrix, averaged current, disorder-induced current fluctuation, and averaged shot noise, which involve different two-Green's-function correlators, can all be derived and computed in an effective and unified way. To test the general applicability of this method, we applied it to compute the transmission coefficient and its fluctuation with a square-lattice tight-binding model and compared with the exact results and other previously proposed approximations. Our results show very good agreement with the exact results for a wide range of disorder concentrations and energies. In addition, to incorporate with density functional theory to realize first-principles quantum transport simulation, we have also derived a general form of
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.
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.
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.
Viscosity in strongly interacting quantum field theories from black hole physics.
Kovtun, P K; Son, D T; Starinets, A O
2005-03-25
The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of variant Planck's over 2pi/4pik(B) for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti-de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids. PMID:15903845
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
Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory
Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Shirokov, A.M.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Ng, E.G.; Yang, C.; Sosonkina, M.; /Ames Lab
2012-06-22
Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.
NASA Astrophysics Data System (ADS)
Simulik, Volodimir
2016-01-01
The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass have been introduced. The axiomatic level description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The 64-dimensional ClR(0,6) algebra in terms of Dirac gamma matrices has been suggested. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory has been found. Different methods of the Dirac equation derivation have been reviewed. The manifestly covariant field equations for an arbitrary spin that follow from the quantum mechanical equations have been considered. The covariant local field theory equations for spin s = (1,1) particle-antiparticle doublet, spin s = (1,0,1,0) particle antiparticle multiplet, spin s = (3/2,3/2) particle-antiparticle doublet, spin s = (2,2) particle-antiparticle doublet, spin s = (2,0,2,0) particle-antiparticle multiplet and spin s = (2,1,2,1) particle-antiparticle multiplet have been introduced. The Maxwell-like equations for the boson with spin s = 1 and nonzero mass have been introduced as well.
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.
Ardehali, M. )
1990-06-15
Some simple inequalities which demonstrate the incompatibility of local realism with quantum theory are derived. They establish, for the first time, necessary conditions for violation of the generalized spin-{ital s} Bell inequalities for a set of three distinct {ital noncoplanar} axes. For {ital s}=1/2, however, these inequalities are equivalent to Wigner's results, thus giving necessary and {ital sufficient} conditions.
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.
Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Wang, Yi-Nan
2015-04-01
We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.
Quantum field theory in curved spacetime and the dark matter problem
Grib, A. A.; Pavlov, Yu. V.
2007-11-14
Quantum field theory in nonstationary curved Friedmann spacetime leads to the phenomenon of creation of massive particles. The hypothesis that in the end of inflation gravitation creates from vacuum superheavy particles decaying on quarks and leptons leading to the observed baryon charge is investigated. Taking the complex scalar field for these particles in analogy with K{sup 0}-meson theory one obtains two components - the long living and short living ones, so that the long living component after breaking the Grand Unification symmetry has a long life time and is observed today as dark matter. The hypothesis that ultra high energy cosmic rays occur as manifestation of superheavy dark matter is considered and some experimental possibilities of the proposed scheme are analyzed.
Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified space
NASA Astrophysics Data System (ADS)
Reinhardt, H.
2016-08-01
The partition function of a relativistic invariant quantum field theory is expressed by its vacuum energy calculated on a spatial manifold with one dimension compactified to a 1-sphere S1(β ), whose circumference β represents the inverse temperature. Explicit expressions for the usual energy density and pressure in terms of the energy density on the partially compactified spatial manifold R2×S1(β ) are derived. To make the resulting expressions mathematically well defined a Poisson resummation of the Matsubara sums as well as an analytic continuation in the chemical potential are required. The new approach to finite-temperature quantum field theories is advantageous in a Hamilton formulation since it does not require the usual thermal averages with the density operator. Instead, the whole finite-temperature behavior is encoded in the vacuum wave functional on the spatial manifold R2×S1(β ). We illustrate this approach by calculating the pressure of a relativistic Bose and Fermi gas and reproduce the known results obtained from the usual grand canonical ensemble. As a first nontrivial application we calculate the pressure of Yang-Mills theory as a function of the temperature in a quasiparticle approximation motivated by variational calculations in Coulomb gauge.
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
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.
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.
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. PMID:27610843
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.
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
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
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)
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.
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.
NASA Astrophysics Data System (ADS)
Das, Ashok; Kalauni, Pushpa
2016-06-01
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter σ (0 ≤σ ≤β ) . We point out new features which arise when σ ≠β/2 in that the Hilbert space develops a natural, modified inner product different from the standard Dirac inner product. We construct the Bogoliubov transformation which connects the doubled vacuum state at zero temperature to the thermal vacuum in this case. We obtain the thermal Green's function (propagator) for the real massive Klein-Gordon theory as an expectation value in this thermal vacuum (with a modified inner product). The factorization of the thermal Green's function follows from this analysis. We also discuss, in the main text as well as in two appendices, various other interesting features which arise in such a description.
From dressed electrons to quasiparticles: The emergence of emergent entities in quantum field theory
NASA Astrophysics Data System (ADS)
Blum, Alexander S.; Joas, Christian
2016-02-01
In the 1970s, the reinterpretation of renormalization group techniques in terms of effective field theories and their subsequent rapid development led to a major reinterpretation of the entire renormalization program, originally formulated in the late 1940s within quantum electrodynamics (QED). A more gradual shift in its interpretation, however, occurred already in the early-to-mid-1950s when renormalization techniques were transferred to solid-state and nuclear physics and helped establish the notion of effective or quasi-particles, emergent entities that are not to be found in the original, microscopic description of the theory. We study how the methods of QED, when applied in different contexts, gave rise to this ontological reinterpretation.
Generalized Multiphoton Quantum Interference
NASA Astrophysics Data System (ADS)
Tillmann, Max; Tan, Si-Hui; Stoeckl, Sarah E.; Sanders, Barry C.; de Guise, Hubert; Heilmann, René; Nolte, Stefan; Szameit, Alexander; Walther, Philip
2015-10-01
Nonclassical interference of photons lies at the heart of optical quantum information processing. Here, we exploit tunable distinguishability to reveal the full spectrum of multiphoton nonclassical interference. We investigate this in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis that decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers.
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
Quantum theory of chemical reactions in the presence of electromagnetic fields.
Tscherbul, T V; Krems, R V
2008-07-21
We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.
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).
Entanglement entropy for non-coplanar regions in quantum field theory
NASA Astrophysics Data System (ADS)
Blanco, David D.; Casini, Horacio
2011-11-01
We study the entanglement entropy in a relativistic quantum field theory for regions which are not included in a single spatial hyperplane. This geometric configuration cannot be treated with the Euclidean time method and the replica trick. Instead, we use a real time method to calculate the entropy for a massive free Dirac field in two dimensions in some approximations. We find some specifically relativistic features of the entropy. First, there is a large enhancement of entanglement due to boosts. As a result, the mutual information between relatively boosted regions does not vanish in the limit of zero volume and large relative boost. We also find extensivity of the information in a deeply Lorentzian regime with large violations of the triangle inequalities for the distances. This last effect is relevant to an interpretation of the amount of entropy enclosed in the Hawking radiation emitted by a black hole.
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.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Generalized Fowler-Nordheim Theory of Field Emission of Carbon Nanotubes
NASA Astrophysics Data System (ADS)
Liang, Shi-Dong; Chen, Lu
2008-07-01
Based on the low-energy band structure of carbon nanotubes (CNs), we develop a generalized Fowler-Nordheim theory of the CN field emission, in which the behavior of the current-voltage (I-V) characteristics depends on the electric field and the diameter of the CNs. This formalism reveals the key differences of field emission between conventional bulk metallic emitters and low-dimensional emitters and gives a clear physical understanding of the non-Fowler-Nordheim feature of the I-V characteristics of the CN field emission.
Generalized Fowler-Nordheim theory of field emission of carbon nanotubes.
Liang, Shi-Dong; Chen, Lu
2008-07-11
Based on the low-energy band structure of carbon nanotubes (CNs), we develop a generalized Fowler-Nordheim theory of the CN field emission, in which the behavior of the current-voltage (I-V) characteristics depends on the electric field and the diameter of the CNs. This formalism reveals the key differences of field emission between conventional bulk metallic emitters and low-dimensional emitters and gives a clear physical understanding of the non-Fowler-Nordheim feature of the I-V characteristics of the CN field emission. PMID:18764229
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).
A general zone theory of color and brightness vision. II. The space-time field.
Bird, J F; Massof, R W
1978-11-01
The elements of vision are brightness and color varying in time and space, constituting a vector space-time function: the visual sensation field. The sensory-field generated from the light-field variations on the retina is analyzed here in terms of elemental space-time responses (Green's functions). Both chromaticity and intensity variations in either time or space are included in a unified theory, to bridge the existing gap between color theory and analyses of spatial and temporal brightness. Sensory Green's functions are here related to standard color models and to familiar responses for special stimuli, and are shown to be advantageous for nonhomogeneous and/or nonstationary visual conditions. The theory is first applied for intensity space-time variations, to elucidate existing intensity-contrast analyses. Then the general theory including chromatic contrast is illustrated by deriving color vision generalizations of the Bloch and Ricco laws and a general space-time reciprocity law, by analyses of wavelength-pulse and color-flicker experiments, and by derivation of Abney's law of luminance additivity for heterochromoatic flicker and minimally distinct borders. PMID:755855
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.
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.
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
NASA Astrophysics Data System (ADS)
Ye, Peng; Gu, Zheng-Cheng
2016-05-01
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state (or atomic insulator) as long as certain global symmetry G is unbroken. At low energies, most of the two-dimensional SPTs with Abelian symmetry can be described by topological quantum field theory (TQFT) of the multicomponent Chern-Simons type. However, in contrast to the fractional quantum Hall effect where TQFT can give rise to interesting bulk anyons, TQFT for SPTs only supports trivial bulk excitations. The essential question in TQFT descriptions for SPTs is to understand how the global symmetry is implemented in the partition function. In this paper, we systematically study TQFT of three-dimensional SPTs with unitary Abelian symmetry (e.g., ZN1×ZN2×... ). In addition to the usual multicomponent B F topological term at level-1, we find that there are new topological terms with quantized coefficients (e.g., a1∧a2∧d a2 and a1∧a2∧a3∧a4 ) in TQFT actions, where a1,a2,... are 1-form U(1) gauge fields. These additional topological terms cannot be adiabatically turned off as long as G is unbroken. By investigating symmetry transformations for the TQFT partition function, we end up with the classification of SPTs that is consistent with the well-known group cohomology approach. We also discuss how to gauge the global symmetry and possible TQFT descriptions of Dijkgraaf-Witten gauge theory.
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)
Grobe, Rainer
2006-03-01
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 Schrödinger'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).
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.
NASA Astrophysics Data System (ADS)
Georgiev, Lachezar S.
2005-02-01
We propose a general and compact scheme for the computation of the periods and amplitudes of the chiral persistent currents, magnetizations and magnetic susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by Aharonov-Bohm magnetic field. This universal approach uses the effective conformal field theory for the edge states in the quantum Hall effect to derive explicit formulas for the corresponding partition functions in presence of flux. We point out the crucial role of a special invariance condition for the partition function, following from the Bloch-Byers-Yang theorem, which represents the Laughlin spectral flow. As an example we apply this procedure to the Z parafermion Hall states and show that they have universal non-Fermi liquid behavior without anomalous oscillations. For the analysis of the high-temperature asymptotics of the persistent currents in the parafermion states we derive the modular S-matrices constructed from the S matrices for the u(1) sector and that for the neutral parafermion sector which is realized as a diagonal affine coset.
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.
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
NASA Astrophysics Data System (ADS)
Lapert, M.; Tehini, R.; Turinici, G.; Sugny, D.
2008-08-01
We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a nonstandard choice of the cost, which is not quadratic in the field. These algorithms can be constructed for pure- and mixed-state quantum systems. The efficiency of the method is shown numerically for molecular orientation with a nonlinearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Dell'Agnello, Simone; Esposito, Giampiero; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
2015-09-01
We first analyze the restricted four-body problem consisting of the Earth, the Moon, and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order 2 mm, whereas for Lagrangian points of unstable
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.
Worldline approach to quantum field theories on flat manifolds with boundaries
NASA Astrophysics Data System (ADS)
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G.
2007-02-01
We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on Bbb R+ × Bbb RD-1 which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full Bbb RD using an image charge. The main technical difficulty lies in the fact that a smooth potential on Bbb R+ × Bbb RD-1 extends to a potential which generically fails to be smooth on Bbb RD. This implies that standard perturbative methods fail and must be improved. We propose a method to deal with this situation. As a result we recover the known heat kernel coefficients on a flat manifold with geodesic boundary, and compute two additional ones, A3 and A7/2. The calculation becomes sensibly harder as the perturbative order increases, and we are able to identify the complete A7/2 with the help of a suitable toy model. Our findings show that the worldline approach is viable on manifolds with boundaries. Certainly, it would be desirable to improve our method of implementing the worldline approach to further simplify the perturbative calculations that arise in the presence of non-smooth potentials.
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.
Fewster, Christopher J
2015-08-01
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.
Cartographic generalization of urban street networks based on gravitational field theory
NASA Astrophysics Data System (ADS)
Liu, Gang; Li, Yongshu; Li, Zheng; Guo, Jiawei
2014-05-01
The automatic generalization of urban street networks is a constant and important aspect of geographical information science. Previous studies show that the dual graph for street-street relationships more accurately reflects the overall morphological properties and importance of streets than do other methods. In this study, we construct a dual graph to represent street-street relationship and propose an approach to generalize street networks based on gravitational field theory. We retain the global structural properties and topological connectivity of an original street network and borrow from gravitational field theory to define the gravitational force between nodes. The concept of multi-order neighbors is introduced and the gravitational force is taken as the measure of the importance contribution between nodes. The importance of a node is defined as the result of the interaction between a given node and its multi-order neighbors. Degree distribution is used to evaluate the level of maintaining the global structure and topological characteristics of a street network and to illustrate the efficiency of the suggested method. Experimental results indicate that the proposed approach can be used in generalizing street networks and retaining their density characteristics, connectivity and global structure.
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dappiaggi, Claudio; Nosari, Gabriele; Pinamonti, Nicola
2016-06-01
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
NASA Astrophysics Data System (ADS)
Basharov, A. M.
2012-09-01
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.
Quantum field theory and the antipodal identification of black-holes
NASA Astrophysics Data System (ADS)
Sanchez, N.; Whiting, B. F.
The antipodal points (U, V, θ, ϕ) and (-U, -V, π - θ, ϕ + π) of the Schwarzchild-Kruskal manifold, usually interpreted as two different events (in two different worlds) are considered here as physically identified (to give one single world). This has fundamental consequences for the QFT formulated on this manifold. The antipodal symmetric fields have (globally) zero norm. The usual particle-antiparticle Fock space definition breaks down. There is no quantum operator (unitary, antiunitary or projection) giving antipodal symmetric states from the usual Kruskal ones. The antipodal symmetric Green functions have the same periodicity β = 8 π M in imaginary (Schwarzschild) time as the usual (non-symmetric) ones. (Identification with ``conical singularity'' would give a period 1/2β). In any case, no usual thermal interpretation is possible for T = β-1 (nor for T0 = 2/β or any other value) in the theory. In the light of these results we discuss ``old'' ideas and more recent ones on identification. Present address: Department of Physics and Astronomy, University of North Carolina-Chapel Hill, NC 27514, USA.
Simmering, Vanessa R; Schutte, Anne R; Spencer, John P
2008-04-01
Within cognitive neuroscience, computational models are designed to provide insights into the organization of behavior while adhering to neural principles. These models should provide sufficient specificity to generate novel predictions while maintaining the generality needed to capture behavior across tasks and/or time scales. This paper presents one such model, the dynamic field theory (DFT) of spatial cognition, showing new simulations that provide a demonstration proof that the theory generalizes across developmental changes in performance in four tasks-the Piagetian A-not-B task, a sandbox version of the A-not-B task, a canonical spatial recall task, and a position discrimination task. Model simulations demonstrate that the DFT can accomplish both specificity-generating novel, testable predictions-and generality-spanning multiple tasks across development with a relatively simple developmental hypothesis. Critically, the DFT achieves generality across tasks and time scales with no modification to its basic structure and with a strong commitment to neural principles. The only change necessary to capture development in the model was an increase in the precision of the tuning of receptive fields as well as an increase in the precision of local excitatory interactions among neurons in the model. These small quantitative changes were sufficient to move the model through a set of quantitative and qualitative behavioral changes that span the age range from 8 months to 6 years and into adulthood. We conclude by considering how the DFT is positioned in the literature, the challenges on the horizon for our framework, and how a dynamic field approach can yield new insights into development from a computational cognitive neuroscience perspective.
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.
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.
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.
Chu Yizen
2009-02-15
Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective Lagrangian for its n-body problem. Perturbation theory is performed about a background Minkowski space-time to O[(v/c){sup 4}] beyond Newtonian gravity, where v is the typical speed of these n particles in their center of energy frame. For the specific case of the 2-body problem, the major efforts underway to measure gravitational waves produced by inspiraling compact astrophysical binaries require their gravitational interactions to be computed beyond the currently known O[(v/c){sup 7}]. We argue that such higher order post-Newtonian calculations must be automated for these field theoretic methods to be applied successfully to achieve this goal. In view of this, we outline an algorithm that would in principle generate the relevant Feynman diagrams to an arbitrary order in v/c and take steps to develop the necessary software. The Feynman diagrams contributing to the n-body effective action at O[(v/c){sup 6}] beyond Newton are derived.
Hebenstreit, F.; Alkofer, R.; Gies, H.
2010-11-15
The nonperturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields E-vector(x-vector,t). Based on the Dirac-Heisenberg-Wigner formalism, we derive a system of partial differential equations of infinite order for the 16 irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field E(t)=E{sub 0} and the Sauter-type electric field E(t)=E{sub 0}sech{sup 2}(t/{tau}). These analytic solutions translate into corresponding expressions within the Dirac-Heisenberg-Wigner formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.
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
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.
Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki
2012-07-27
We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.
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.
"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. PMID:21073210
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.
Studies in Quantum Field Theory. Final Report, July 21, 1992 - July 31, 1999
Caldi, Daniel G.
2001-03-31
Mechanisms have been investigated for chiral symmetry breaking in QED and non-abelian gauge theories using the Schwinger proper-time formalism. Multi-soliton and plane-wave solutions have been generated in affine Toda field theories. New predictions for neutrino mass generation via superfluid-type condensates in the Electroweak theory have been made. Solutions for the linear inhomogeneous bioheat equation were studied in cylindrical geometries.
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.
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
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.
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.
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.
Quantum Paradoxes: Quantum Theory for the Perplexed
NASA Astrophysics Data System (ADS)
Aharonov, Yakir; Rohrlich, Daniel
2003-09-01
A Guide through the Mysteries of Quantum Physics! Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich of the Weizmann Institute, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language. More than 200 problem sets introduce readers to the concepts and implications of quantum mechanics that have arisen from the experimental results of the recent two decades. With students as well as researchers in mind, the authors give an insight into that part of the field, which led Feynman to declare that "nobody understands quantum mechanics". For a solutions manual, lecturers should contact the editorial department at vch-physics@wiley-vch.de, stating their affiliation and the course in which they wish to use the book.
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.
Reductionism, emergence, and effective field theories
NASA Astrophysics Data System (ADS)
Castellani, Elena
In recent years, a "change in attitude" in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
Tavernelli, Ivano; Curchod, Basile F. E.; Rothlisberger, Ursula
2010-05-15
A mixed quantum-classical method aimed at the study of nonadiabatic dynamics in the presence of external electromagnetic fields is developed within the framework of time-dependent density functional theory. To this end, we use a trajectory-based description of the quantum nature of the nuclear degrees of freedom according to Tully's fewest switches trajectories surface hopping, where both the nonadiabatic coupling elements between the different potential energy surfaces, and the coupling with the external field are given as functionals of the ground-state electron density or, equivalently, of the corresponding Kohn-Sham orbitals. The method is applied to the study of the photodissociation dynamics of some simple molecules in gas phase.
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.
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
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.
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
NASA Astrophysics Data System (ADS)
The field of many-body quantum physics has a long history of fundamental discoveries, many of which have gone far beyond our wildest imagination. These include the study of novel states of matter, the observation of previously unseen phase transitions, and the discovery of new macroscopic quantum effects which arise when the intriguing rules of quantum mechanics are no longer restricted to the subatomic world, but rather determine the collective behavior of systems that are observable with the naked eye. In the past, it has often been proven difficult to obtain the underlying theory that yields an accurate description of the collective quantum phenomenon on the microscopic level. A good example is the discovery of superfluidity in liquid 4He by Pyotr Kapitsa, John Allen and Don Misener in 1938 [1, 2], where superfluidity refers to the fact that the liquid can flow without experiencing resistance, which leads for example to the spectacular fountain effect [3]. Since the atoms interact very strongly, the precise internal state of liquid helium is notoriously difficult to determine.
Hierarchical theory of quantum adiabatic evolution
NASA Astrophysics Data System (ADS)
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
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.
Barnett, Stephen M.; Cresser, James D.
2005-08-15
We present a Markovian quantum theory of friction. Our approach is based on the idea that collisions between a Brownian particle and single molecules of the surrounding medium constitute, as far as the particle is concerned, instantaneous simultaneous measurements of its position and momentum.
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.
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.
Tureanu, Anca
2006-09-15
In the framework of quantum field theory on noncommutative space-time with the symmetry group O(1,1)xSO(2), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the 2{yields}2-scattering amplitude in cos {theta}, {theta} being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross section are also presented.
The Quantum Theory of the Free Maxwell Field on the de Sitter Expanding Universe
NASA Astrophysics Data System (ADS)
Cotăescu, I. I.; Crucean, C.
2010-12-01
The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves solutions of the Maxwell equation which are eigenfunctions of the energy operator. Such particular solutions complete the theory in which only the solutions of given momentum were considered so far. The energy eigenfunctions can be obtained thanks to our new time-evolution picture proposed previously for the scalar and Dirac fields. Considering both these types of modes, it is shown that the second quantization of the free electromagnetic potential in the Coulomb gauge can be done in a canonical manner as in special relativity. The principal conserved one-particle operators associated to Killing vectors are derived, concentrating on the energy, momentum and total angular momentum operators.
Orthodontics in a quantum world III: electromagnetic field theory and oral parafunction.
James, Gavin
2008-01-01
The study of electromagnetic field theory and bioenergy has established that there is an extensive communication system throughout the body by way of a functional matrix. This enables the body to use the mouth to assist it during the expenditure of effort elsewhere in the body. A variety of oral behaviors can be identified as contributing to this. To some extent, these behaviors indicate where an imbalance is present in the body.
Grimme, Stefan
2014-10-14
A black-box type procedure is presented for the generation of molecule-specific, classical potential energy functions (force-field, FF) solely from quantum mechanically (QM) computed input data. The approach can treat covalently bound molecules and noncovalent complexes with almost arbitrary structure. The necessary QM information consists of the equilibrium structure and the corresponding Hessian matrix, atomic partial charges, and covalent bond orders. The FF fit is performed automatically without any further input and yields a specific (nontransferable) potential which very closely resembles the QM reference potential near the equilibrium. The resulting atomistic, fully flexible FF is anharmonic and allows smooth dissociation of covalent bonds into atoms. A newly proposed force-constant-bond-energy relation with little empiricism provides reasonably accurate (about 5-10% error) atomization energies for almost arbitrary diatomic and polyatomic molecules. Intra- and intermolecular noncovalent interactions are treated by using well established and accurate D3 dispersion coefficients, CM5 charges from small basis set QM calculations, and a new interatomic repulsion potential. Particular attention has been paid to the construction of the torsion potentials which are partially obtained from automatic QM-tight-binding calculations for model systems. Detailed benchmarks are presented for conformational energies, atomization energies, vibrational frequencies, gas phase structures of organic molecules, and transition metal complexes. Comparisons to results from standard FF or semiempirical methods reveal very good accuracy of the new potential. While further studies are necessary to validate the approach, the initial results suggest QMDFF as a routine tool for the computation of a wide range of properties and systems (e.g., for molecular dynamics of isolated molecules, explicit solvation, self-solvation (melting) or even for molecular crystals) in particular when standard
Grimme, Stefan
2014-10-14
A black-box type procedure is presented for the generation of molecule-specific, classical potential energy functions (force-field, FF) solely from quantum mechanically (QM) computed input data. The approach can treat covalently bound molecules and noncovalent complexes with almost arbitrary structure. The necessary QM information consists of the equilibrium structure and the corresponding Hessian matrix, atomic partial charges, and covalent bond orders. The FF fit is performed automatically without any further input and yields a specific (nontransferable) potential which very closely resembles the QM reference potential near the equilibrium. The resulting atomistic, fully flexible FF is anharmonic and allows smooth dissociation of covalent bonds into atoms. A newly proposed force-constant-bond-energy relation with little empiricism provides reasonably accurate (about 5-10% error) atomization energies for almost arbitrary diatomic and polyatomic molecules. Intra- and intermolecular noncovalent interactions are treated by using well established and accurate D3 dispersion coefficients, CM5 charges from small basis set QM calculations, and a new interatomic repulsion potential. Particular attention has been paid to the construction of the torsion potentials which are partially obtained from automatic QM-tight-binding calculations for model systems. Detailed benchmarks are presented for conformational energies, atomization energies, vibrational frequencies, gas phase structures of organic molecules, and transition metal complexes. Comparisons to results from standard FF or semiempirical methods reveal very good accuracy of the new potential. While further studies are necessary to validate the approach, the initial results suggest QMDFF as a routine tool for the computation of a wide range of properties and systems (e.g., for molecular dynamics of isolated molecules, explicit solvation, self-solvation (melting) or even for molecular crystals) in particular when standard
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.
Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets
NASA Astrophysics Data System (ADS)
Sverdlov, Roman
2009-05-01
This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time to causal sets.
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.
Interpretation neutrality in the classical domain of quantum theory
NASA Astrophysics Data System (ADS)
Rosaler, Joshua
2016-02-01
I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.
NASA Astrophysics Data System (ADS)
Lyo, S. K.
1989-10-01
The effect of carrier-impurity interactions on luminescence- and excitation-spectroscopy line shapes and the Landau-level spectral density in a strong quantizing magnetic field is examined in modulation-doped semiconductor quantum wells. The line-shape function is obtained by summing the ``ladder diagrams,'' extending our previous ``one-rung'' approximation. Apart from yielding a line broadening, the carrier-impurity interaction is found to induce off-diagonal transitions (ODT) (n-->n' n'≠n) between the Landau levels in the conduction and valence bands, breaking the usual n-->n selection rule. Here the first and second integers indicate the Landau quantum numbers in the conduction (valence) and valence (conduction) bands, respectively, for luminescence (excitation), for example, in an n-type system. The Landau-level spectral density (essential for obtaining the line-shape functions) is investigated by a self-consistent Born approximation which includes inter-Landau-level impurity scattering. The theory is applied to an n-type strained InxGa1-xAs/GaAs quantum well, where optical transitions arise between the conduction band and the strain-split in-plane ``light-hole'' band. For excitation spectra, the theory predicts that ODT introduce lines below the usual nF-->nF threshold transition as well as satellite lines between the usual main n-->n lines above the threshold (i.e., n>=nF). Here nF is the quantum number of the lowest-lying empty or partially filled conduction-band Landau level. The luminescence line shape is dominated by ODT 1, 2,...-->0 (in addition to the main 0-->0 transition) at low temperatures and by the usual n-->n transitions at high temperatures. The accuracy of the ``one-rung'' approximation is assessed.
Equilibration properties of classical integrable field theories
NASA Astrophysics Data System (ADS)
De Luca, Andrea; Mussardo, Giuseppe
2016-06-01
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper \\hslash \\to 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the generalized Gibbs ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the inverse scattering method.
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. PMID:25871066
NASA Astrophysics Data System (ADS)
Gueron, Jorge; Leston, Mauricio
2013-08-01
During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of λΦ4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example — although does not capture all the difficulties in the constructive quantum field theory approach — allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach.
Quantum Probability Theory and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Fröhlich, Jürg; Schubnel, Baptiste
By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).
NASA Astrophysics Data System (ADS)
Robles Pérez, S. J.
2013-02-01
The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of whether the complementary principle of quantum mechanics has to be extended to the quantum description of the whole space-time manifold. If so, the particle description entails the consideration of a multiverse scenario and the wave description induces us to consider as well correlations and interactions among the universes of the multiverse.
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
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.
Quantum fields with classical perturbations
Dereziński, Jan
2014-07-15
The main purpose of these notes is a review of various models of Quantum Field Theory (QFT) involving quadratic Lagrangians. We discuss scalar and vector bosons, spin 1/2 fermions, both neutral and charged. Beside free theories, we study their interactions with classical perturbations, called, depending on the context, an external linear source, mass-like term, current or electromagnetic potential. The notes may serve as a first introduction to QFT.
Informational derivation of quantum theory
NASA Astrophysics Data System (ADS)
Chiribella, Giulio; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2011-07-01
We derive quantum theory from purely informational principles. Five elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—define a broad class of theories of information processing that can be regarded as standard. One postulate—purification—singles out quantum theory within this class.
Informational derivation of quantum theory
Chiribella, Giulio; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2011-07-15
We derive quantum theory from purely informational principles. Five elementary axioms - causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning - define a broad class of theories of information processing that can be regarded as standard. One postulate - purification - singles out quantum theory within this class.
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{sub 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{sub 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.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
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)
Freericks, J. K.; Han, Shuyang; Mikelsons, Karlis; Krishnamurthy, H. R.
2016-08-01
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher temperatures, in the normal phase, it shows why the local density approximation works so well, since the local density and generalized gradient approximations are essentially indistinguishable from each other (and from the exact solution within full inhomogeneous dynamical mean-field theory). But because the generalized gradient expansion only involves nearest-neighbor corrections, it does not work as well at low temperatures, when the systems enter into ordered phases. This is primarily due to the problem that ordered phases often satisfy some global constraints, which determine the spatial ordering pattern, and the local density and generalized gradient approximations are not able to impose those kinds of constraints; they also overestimate the tendency to order. The theory is applied to phase separation of different mass fermionic mixtures represented by the Falicov-Kimball model and to determining the entropy per particle of a fermionic system represented by the Hubbard model. The generalized gradient approximation is a useful diagnostic for the accuracy of the local density approximation—when both methods agree, they are likely accurate, when they disagree, neither is likely to be correct.
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.
Frames, designs, and spherical codes in quantum information theory
NASA Astrophysics Data System (ADS)
Renes, Joseph M.
Frame theory offers a lens through which to view a large portion of quantum information theory, providing an organizational principle to those topics in its purview. In this thesis, I cut a trail from foundational questions to practical applications, from the origin of the quantum probability rule to quantum cryptography, by way of a standard quantum measurement helpful in quantum tomography and representation of quantum theory. Before embarking, preparations are undertaken by outlining the relevant aspects of frame theory, particularly the characterization of generalized orthonormal bases in terms of physical quantum measurements, as well as several aesthetically appealing families of measurements, each possessing a high degree of symmetry. Much more than just elegant, though, these quantum measurements are found to be useful in many aspects of quantum information theory. I first consider the foundational question of justifying the quantum probability rule, showing that putting a probability valuation on generalized quantum measurements leads directly to the Born rule. Moreover, for qubits, the case neglected in the traditional formulation of Gleason's theorem, a symmetric three-outcome measurement called the trine is sufficient to impel the desired form. Keeping with foundational questions, I then turn to the problem of establishing a symmetric measurement capable of effortlessly rendering quantum theory in terms of classical probability theory. Numerical results provide an almost utterly convincing amount of evidence for this, justifying the subsequent study of its use in quantum tomography and detailed account of the properties of the reduction to probabilistic terms. Saving perhaps the most exciting topic for last, I make use of these aesthetic ensembles in the applied field of quantum cryptography. A large class of streamlined key distribution protocols may be cut from the cloth of these ensembles, and their symmetry affords them improved tolerance to
Adiabatic Quantum Computation and the Theory of Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Kaminsky, William; Lloyd, Seth
2007-03-01
We present a general approach to determining the asymptotic scaling of adiabatic quantum computational resources (space, time, energy, and precision) on random instances of NP-complete graph theory problems. By utilizing the isomorphisms between certain NP-complete graph theory problems and certain frustrated spin models, we demonstrate that the asymptotic scaling of the minimum spectral gap that determines the asymptotic running time of adiabatic algorithms is itself determined by the presence and character of quantum phase transitions in these frustrated models. Most notably, we draw the conclusion that adiabatic quantum computers based on quantum Ising models are much less likely to be efficient than those based on quantum rotor or Heisenberg models. We then exhibit practical rotor and Heisenberg model based architectures using Josephson junction and quantum dot circuits.
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.
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.
Matrix field theory: Applications to superconductivity
NASA Astrophysics Data System (ADS)
Zhou, Lubo
In this thesis a systematic, functional matrix field theory is developed to describe both clean and disordered s-wave and d-wave superconductors and the quantum phase transitions associated with them. The thesis can be divided into three parts. The first part includes chapters 1 to 3. In chapter one a general physical introduction is given. In chapters two and three the theory is developed and used to compute the equation of state as well as the number-density susceptibility, spin-density susceptibility, the sound attenuation coefficient, and the electrical conductivity in both clean and disordered s-wave superconductors. The second part includes chapter four. In this chapter we use the theory to describe the disorder-induced metal - superconductor quantum phase transition. The key physical idea here is that in addition to the superconducting order-parameter fluctuations, there are also additional soft fermionic fluctuations that are important at the transition. We develop a local field theory for the coupled fields describing superconducting and soft fermionic fluctuations. Using simple renormalization group and scaling ideas, we exactly determine the critical behavior at this quantum phase transition. Our theory justifies previous approaches. The third part includes chapter five. In this chapter we study the analogous quantum phase transition in disordered d-wave superconductors. This theory should be related to high Tc superconductors. Surprisingly, we show that in both the underdoped and overdoped regions, the coupling of superconducting fluctuations to the soft disordered fermionic fluctuations is much weaker than that in the s-wave case. The net result is that the disordered quantum phase transition in this case is a strong coupling, or described by an infinite disordered fixed point, transition and cannot be described by the perturbative RG description that works so well in the s-wave case. The transition appears to be related to the one that occurs in
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.
General relativistic theory of light propagation in the field of gravitational multipoles
NASA Astrophysics Data System (ADS)
Korobkov, Pavel
We consider propagation of electromagnetic signals through the time-dependent gravitational field of an isolated astronomical system emitting gravitational waves. The system is assumed to possess multipole moments of arbitrary order. Working in the linear, weak-field approximation of general relativity, we obtain analytical expressions for light-ray trajectory and observable effects of bending of light, time delay, and gravitational rotation of the polarization plane. The relative positions of the source of light, the isolated system, and the observer are not restricted, which makes our formalism quite general and applicable for most practical situations. Asymptotic expressions for observable effects are obtained in two limiting cases of arrangement of light source, observer, and the source of gravitational waves: the gravitational-lens approximation and the approximation of plane gravitational waves. It is shown that in the gravitational-lens approximation the leading contributions to the effects due to multipole moments of arbitrary order fall off with the impact parameter as 1/d2 and 1/d3 for time delay and deflection of light respectively. Such, stronger than it could be a priori expected, dependance on impact parameter hinders observation of time-dependent effects in gravitational lensing. In the plane-gravitational-wave approximation the expressions for observable effects due to gravitational waves of arbitrary multipolarity are obtained in terms of the transverse-traceless (TT) part of the spacial components of the metric tensor.
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.
Theory of Quantum Hall Nematics
NASA Astrophysics Data System (ADS)
Radzihovsky, Leo; Dorsey, Alan T.
2002-05-01
Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a ``quantum Hall nematic'' (QHN) phase, predict the existence of a novel, highly anisotropic q3 density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model.
Theory of quantum Hall nematics.
Radzihovsky, Leo; Dorsey, Alan T
2002-05-27
Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a "quantum Hall nematic" (QHN) phase, predict the existence of a novel, highly anisotropic q(3) density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model. PMID:12059490
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.
Energy flow in non-equilibrium conformal field theory
NASA Astrophysics Data System (ADS)
Bernard, Denis; Doyon, Benjamin
2012-09-01
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.
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.
Generalized effective description of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Gupt, Brajesh
2015-10-01
The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big bang singularity. Originally, this description was derived using Gaussian quantum states with small dispersions. In this paper we present a generalization to incorporate states with large dispersions. Specifically, we derive the generalized effective Friedmann and Raychaudhuri equations and propose a generalized effective Hamiltonian which are being used in an ongoing study of the phenomenological consequences of a broad class of quantum geometries. We also discuss an interesting interplay between the physics of states with larger dispersions in standard LQC, and of sharply peaked states in (hypothetical) LQC theories with larger area gap.
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.
Kac Moody theories for colored phase space (quantum Hall) droplets
NASA Astrophysics Data System (ADS)
Polychronakos, Alexios P.
2005-04-01
We derive the canonical structure and Hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza-Klein construction on the phase space. The emerging theory is a nonlinear higher-dimensional generalization of the gauged Kac-Moody algebra. To leading order in ℏ this reproduces the edge state chiral Wess-Zumino-Witten action of the droplets.
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.
NASA Astrophysics Data System (ADS)
Diehl, S.; Baranov, M.; Daley, A. J.; Zoller, P.
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).10.1103/PhysRevB.82.064509]. 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.
Supergrassmannian and large N limit of quantum field theory with bosons and fermions
Konechny, Anatoly; Turgut, O. Teoman
2002-03-01
We study a large N{sub c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.
Quartic quantum theory: an extension of the standard quantum mechanics
NASA Astrophysics Data System (ADS)
Życzkowski, Karol
2008-09-01
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher-dimensional convex body {\\cal M}_N^Q of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in the N-dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalization of the standard quantum theory for which K = N2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N.
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.
General model of phospholipid bilayers in fluid phase within the single chain mean field theory.
Guo, Yachong; Pogodin, Sergey; Baulin, Vladimir A
2014-05-01
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.
All possible local charges in a local quantum field theory: Massive case
NASA Astrophysics Data System (ADS)
Amigó, J. M.
1988-04-01
A proof for local charges of the classical result first put forward by Coleman and Mandula [Phys. Rev. 159, 1251 (1967)] is given. Local charges are operators defined as integrals of the time component of conserved Hermitian density currents; in interacting theories they happen to be generators of symmetries of the S matrix.
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
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.
NASA Astrophysics Data System (ADS)
Lapert, M.; Tehini, R.; Turinici, G.; Sugny, D.
2009-06-01
We propose a monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration, the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using bandpass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse-shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.
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 presence of a medium: Green's function expansions
Kheirandish, Fardin; Salimi, Shahriar
2011-12-15
Starting from a Lagrangian and using functional-integration techniques, series expansions of Green's function of a real scalar field and electromagnetic field, in the presence of a medium, are obtained. The parameter of expansion in these series is the susceptibility function of the medium. Relativistic and nonrelativistic Langevin-type equations are derived. Series expansions for Lifshitz energy in finite temperature and for an arbitrary matter distribution are derived. Covariant formulations for both scalar and electromagnetic fields are introduced. Two illustrative examples are given.
Quantum theory of optical coherence of nonstationary light in the space-frequency domain
Lahiri, Mayukh; Wolf, Emil
2010-10-15
Classical theories of coherence for statistically stationary, as well as, nonstationary optical fields are frequently discussed both in the space-time and in the space-frequency domains. However, the quantum treatment of coherence theory is generally carried out in the space-time domain. In this paper, we present a quantum-mechanical theory of first-order coherence for statistically nonstationary light in the space-frequency domain.
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
NASA Astrophysics Data System (ADS)
Stottmeister, Alexander; Thiemann, Thomas
2016-06-01
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Scale invariance, conformality, and generalized free fields
NASA Astrophysics Data System (ADS)
Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; Luty, Markus A.; Prilepina, Valentina
2016-02-01
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that 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). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.
Quantum theory on protein folding
NASA Astrophysics Data System (ADS)
Luo, LiaoFu
2014-03-01
The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. It is shown that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation-transition Hamiltonian the nonradiative matrix element was calculated and a general formulas for protein folding rate was deduced. The analytical form of the formula was utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation was interpreted. By using temperature dependence data the multi-torsion correlation was studied. The decoherence time of quantum torsion state is estimated. The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.
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.
NASA Astrophysics Data System (ADS)
Banerjee, D.; Bögli, M.; Hofmann, C. P.; Jiang, F.-J.; Widmer, P.; Wiese, U.-J.
2016-09-01
We present detailed analytic calculations of finite-volume energy spectra, mean-field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. An emergent approximate spontaneously broken SO(2 ) symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phononlike excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.
Quantum-classical dynamics of wave fields.
Sergi, Alessandro
2007-02-21
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surface-hopping approximations. Hence, the results obtained follow qualitatively those of previous surface-hopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantum-classical wave fields proposed here is a straightforward non-Hamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.
Bothe's 1925 heuristic assumption in the dawn of quantum field theory
NASA Astrophysics Data System (ADS)
Fick, D.
2013-01-01
In an unpublished manuscript filed at the Archive of the Max-Planck Society in Berlin, Walther Bothe (1891-1957) put, with one heuristic assumption, the spontaneous and induced transitions of light quanta, on an equal footing, probably as early as 1925. In modern terms, he assumed that the probability for the creation of a light quantum in a phase space cell already containing s light quanta is proportional to s + 1 and not, as assumed at that time, proportional to s; that is proportional to the fraction of the total radiation density which belongs to s light quanta. For Bothe, the added +1 somehow replaced the spontaneous decay and allowed him to treat empty phase space cells in a black body as thermodynamically consistent. We describe in some detail Bothe's route to this heuristic trick. Finally we discuss why, both Bose's and Bothe's heuristic assumptions lead to an identical distribution law for light quanta in a black body and thus to Planck's law and Einstein's fluctuation formula.
The XXth International Workshop High Energy Physics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
The Workshop continues a series of workshops started by the Skobeltsyn Institute of Nuclear Physics of Lomonosov Moscow State University (SINP MSU) in 1985 and conceived with the purpose of presenting topics of current interest and providing a stimulating environment for scientific discussion on new developments in theoretical and experimental high energy physics and physical programs for future colliders. Traditionally the list of workshop attendees includes a great number of active young scientists and students from Russia and other countries. This year Workshop is organized jointly by the SINP MSU and the Southern Federal University (SFedU) and will take place in the holiday hotel "Luchezarniy" (Effulgent) situated on the Black Sea shore in a picturesque natural park in the suburb of the largest Russian resort city Sochi - the host city of the XXII Olympic Winter Games to be held in 2014. The main topics to be covered are: Experimental results from the LHC. Tevatron summary: the status of the Standard Model and the boundaries on BSM physics. Future physics at Linear Colliders and super B-factories. Extensions of the Standard Model and their phenomenological consequences at the LHC and Linear Colliders: SUSY extensions of the Standard Model; particle interactions in space-time with extra dimensions; strings, quantum groups and new ideas from modern algebra and geometry. Higher order corrections and resummations for collider phenomenology. Automatic calculations of Feynman diagrams and Monte Carlo simulations. LHC/LC and astroparticle/cosmology connections. Modern nuclear physics and relativistic nucleous-nucleous collisions.
Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
Mestre, Angela
2010-08-15
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle irreducible n-point function in terms of its loop order contributions. The algebraic representation is so that graphs can be evaluated as Feynman graphs.
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.
Combinatorics of n-point functions via Hopf algebra in quantum field theory
Mestre, Angela; Oeckl, Robert
2006-05-15
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more intrinsic and leads to efficient algorithms suitable for concrete computations. It may also be used to efficiently perform tree level computations.
Holographic effective field theories
NASA Astrophysics Data System (ADS)
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
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.
Hilbert's projective metric in quantum information theory
NASA Astrophysics Data System (ADS)
Reeb, David; Kastoryano, Michael J.; Wolf, Michael M.
2011-08-01
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or positive partial transpose operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under protocols involving local quantum operations and classical communication or under other cone-preserving operations. The results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels, for instance, improving Ruskai's trace-norm contraction inequality. A new duality between distinguishability measures and base norms is provided. For two given pairs of quantum states we show that the contraction of Hilbert's projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other. Inequalities between Hilbert's projective metric and the Chernoff bound, the fidelity and various norms are proven.
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)
Bipartite field theories from D-branes
NASA Astrophysics Data System (ADS)
Franco, Sebastián; Uranga, Angel
2014-04-01
We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, = 1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.
The decoupling approach to quantum information theory
NASA Astrophysics Data System (ADS)
Dupuis, Frédéric
2010-04-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently 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.
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.
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 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
NASA Astrophysics Data System (ADS)
Gushchin, A. A.
1982-12-01
CONTENTSIntroduction § 1. Basic notation and definitions § 2. The Doléans measure and increasing fields § 3. Theorems on predictable projections. Decomposition of weak submartingales § 4. Weakly predictable random fields § 5. Theorems on weakly predictable projections § 6. Decomposition of strong martingales References
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.
A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Chiu, Jui-Yu; Jain, Ambar; Neill, Duff; Rothstein, Ira Z.
2012-05-01
Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the relevant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. Such observables include: transverse momentum distributions at p T much less then the high energy scattering scale, jet broadening, exclusive hadroproduction and decay, as well as the Sudakov form factor. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any sce- nario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form fac- tor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are universal. We present details of the factorization and re- summation of the jet broadening cross section including a renormalization in p ⊥ space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to
Theory of Nematic Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
2014-10-01
We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has z =2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic fractional quantum Hall fluid into a nematic fractional quantum Hall phase. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. On the other hand, Laughlin quasiparticles and the Kohn collective mode remain gapped at this quantum phase transition, and Kohn's theorem is satisfied. The leading couplings between the nematic order parameter and the gauge fields include a term of the same form as the Wen-Zee term. A disclination of the nematic order parameter carries an unquantized electric charge. We also discuss the relation between nematic degrees of freedom and the geometrical response of the fractional quantum Hall fluid.
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.
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 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. PMID:17995307
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.
Theory of Quantum Hall Nematics
NASA Astrophysics Data System (ADS)
Radzihovsky, Leo; Dorsey, Alan
2002-03-01
Transport measurements on two dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally-ordered, compressible liquid state. We develop and analyze [1] a microscopic theory of such a ``quantum Hall nematic'' (QHN) phase, predict the existence of a novel, highly anisotropic q^3 density-director mode, find that the T=0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model. This research was supported by NSF DMR-9978547, DMR-9625111, and the Sloan and Packard Foundations. [1] L. Radzihovsky and A. T. Dorsey, cond-mat/0110083
NASA Astrophysics Data System (ADS)
Ginzburg, V. B.
1996-09-01
A toroidal spiral field is introduced that propagates around all the objects in the universe. The nature of this field can be either gravitational or electrostatic or magnetic, and it governs the motion of the objects as well as the forces that act upon them. The topology of the toroidal spiral field is obtained when the Bertrami vortex comprised of two helical fluxes of opposite vorticity is curved into a circle. The main parameter that defines the geometry of the toroidal spiral field is the inversion radius of a sphere at which the toroidal fluxes of opposite vorticity meet. The inversion sphere is the border surface at which the matter converts into anti-matter, and at which the law of physics are inverted. The theory covers the problem of two objects orbiting each other with possible sizes ranging from an elementary particle to a black hole and to a galaxy. The equations obtained define the radii of the stationary quantum orbits which can be applied to a structure of the hydrogen atom, including its nucleus, as well as to a structure of a planetary system and a black hole. They also establish the relativistic relationships for the gravitational and inertial masses as well as for the electrical charge which are quite different than those proposed by Lorentz.
No extension of quantum theory can have improved predictive power.
Colbeck, Roger; Renner, Renato
2011-01-01
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. PMID:21811240
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.
On the renormalization of non-commutative field theories
NASA Astrophysics Data System (ADS)
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Quantum hall effect at low magnetic fields
Huckestein
2000-04-01
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of the quantum Hall effect, are in fact in agreement with the standard theory. The apparent low-field transition observed in the experiments is identified as a crossover due to weak localization and a strong reduction of the conductivity when Landau quantization becomes dominant.
Hydrodynamic theory of quantum fluctuating superconductivity
NASA Astrophysics Data System (ADS)
Davison, Richard A.; Delacrétaz, Luca V.; Goutéraux, Blaise; Hartnoll, Sean A.
2016-08-01
A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-type peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short-range density-density interactions. This leads to an effective field theoretic and fully quantum derivation of a classic result on flux flow resistance. With strong breaking of time-reversal invariance, the optical conductivity exhibits what we call a "hydrodynamic supercyclotron" resonance. We obtain the frequency and decay rate of this resonance for the case of supercurrent relaxation due to an emergent Chern-Simons gauge field. The supercurrent decay rate in this "topologically ordered superfluid vortex liquid" is determined by the conductivities of the normal fluid component, rather than the vortex core.
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
2016-07-01
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.
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.
Theory of quantum gravity beyond Einstein and space-time dynamics with quantum inflation
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2015-10-01
In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A bi-frame space-time is initiated to describe the laws of nature. One frame space-time is a globally flat coordinate Minkowski space-time that acts as an inertial reference frame for the motions of fields, the other is a locally flat non-coordinate Gravifield space-time that functions as an interaction representation frame for the degrees of freedom of fields. The Gravifield is sided on both the globally flat coordinate space-time and locally flat non-coordinate space-time and characterizes the gravitational force. Instead of the principle of general coordinate invariance in Einstein theory of general relativity, some underlying principles with the postulates of coordinate independence and gauge invariance are motivated to establish the theory of quantum gravity. When transmuting the Gravifield basis into the coordinate basis in Minkowski space-time, it enables us to obtain equations of motion for all quantum fields and derive basic conservation laws for all symmetries. The gravity equation is found to be governed by the total energy-momentum tensor defined in the flat Minkowski space-time. When the spinnic and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we arrive at a Lorentz invariant and conformally flat background Gravifield space-time that is characterized by a cosmic vector with a non-zero cosmological mass scale. We also obtain the massless graviton and massive spinnon. The resulting universe is in general not isotropic in terms of conformal proper time and turns out to be inflationary in light of cosmic proper time. The conformal size of the universe has a singular at the cosmological horizon to which the cosmic proper time must be infinitely
Quantum Walks: Theory, Application, and Implementation
NASA Astrophysics Data System (ADS)
Schmitz, Albert Thomas
The quantum walk is a method for conceptualizing and designing quantum computing algorithms and it comes in two forms: the continuous-time and discrete-time quantum walk. The thesis is organized into three parts, each of which looks to develop the concept and uses of the quantum walk. The first part is the theory of the quantum walk. This includes definitions and considerations for the various incarnations of the discrete-time quantum walk and a discussion on the general method for connecting the continuous-time and discrete-time versions. As a result, it is shown that most versions of the discrete-time quantum walk can be put into a general form and this can be used to simulate any continuous-time quantum walk. The second part uses these results for a hypothetical application. The application presented is a search algorithm that appears to scale in the time for completion independent of the size of the search space. This behavior is then elaborated upon and shown to have general qualitative agreement with simulations to within the approximations that are made. The third part introduces a method of implementation. Given a universal quantum computer, the method is discussed and shown to simulate an arbitrary discrete-time quantum walk. Some of the benefits of this method are that half the unitary evolution can be achieved without the use of any gates and there may be some possibility for error detection. The three parts combined suggest a possible experiment, given a quantum computing scheme of sufficient robustness.
Unification of quantum theory and classical physics
Stapp, H.P.
1985-07-01
A program is described for unifying quantum theory and classical physics on the basis of the Copenhagen-interpretation idea of external reality and a recently discovered classical part of the electromagnetic field. The program effects an integration of the intuitions of Heisenberg, Bohr, and Einstein.
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.
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.
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.
String Theory, Unification and Quantum Gravity
NASA Astrophysics Data System (ADS)
Stelle, K. S.
An overview is given of the way in which the unification program of particle physics has evolved into the proposal of superstring theory as a prime candidate for unifying quantum gravity with the other forces and particles of nature. A key concern with quantum gravity has been the problem of ultraviolet divergences, which is naturally solved in string theory by replacing particles with spatially extended states as the fundamental excitations. String theory turns out, however, to contain many more extended-object states than just strings. Combining all this into an integrated picture, called M-theory, requires recognition of the rôle played by a web of nonperturbative duality symmetries suggested by the nonlinear structures of the field-theoretic supergravity limits of string theory.
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.
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)
Kwak, Seung Ki
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time coordinates. Recently developed double field theory is motivated from this idea and it implements T-duality manifestly by doubling the coordinates. In this thesis we will mainly focus on the double field theory formulation of different string theories in its low energy limit: bosonic, heterotic, type II and its massive extensions, and N = 1 supergravity theory. In chapter 2 of the thesis we study the equivalence of different formulations of double field theory. There are three different formulations of double field theory: background field E formulation, generalized metric H formulation, and frame field EAM formulation. Starting from the frame field formalism and choosing an appropriate gauge, the equivalence of the three formulations of bosonic theory are explicitly verified. In chapter 3 we construct the double field theory formulation of heterotic strings. The global symmetry enlarges to O( D, D + n) for heterotic strings and the enlarged generalized metric features this symmetry. The structural form of bosonic theory can directly be applied to the heterotic theory with the enlarged generalized metric. In chapter 4 we develop a unified framework of double field theory for type II theories. The Ramond-Ramond potentials fit into spinor representations of the duality group O( D, D) and the theory displays Spin+( D, D) symmetry with its self-duality relation. For a specific form of RR 1-form the theory reduces to the massive deformation of type IIA theory due to Romans. In chapter 5 we formulate the N = 1 supersymmetric extension of double field theory including the coupling to n abelian vector multiplets. This theory features a local O(1, 9 + n) x O(1, 9) tangent space symmetry under which the fermions transform. (Copies available exclusively from
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.
Quantum Theory of Atom Laser Cooling
NASA Astrophysics Data System (ADS)
Wu, Xiang-Yao; Zhang, Bai-Jun; Yang, Jing-Hai; Liu, Xiao-Jing; Wu, Yi-Heng; Wang, Qing-Cai; Wang, Yan; Ba, Nuo; Li, Jing-Wu
2011-09-01
In this paper, we study the laser cooling mechanisms with extended Schrodinger quantum wave equation, which can describe a particle in conservative and non-conservative force field. We prove the atom in laser field can be cooled with the theory, and predict that the atom cooling temperature T is directly proportional to the atom vibration frequency ω, which are in accordance with experiment results (A.D. Oconnell, et al. in Nature 464:697, 2010).
Diffeomorphisms in group field theories
Baratin, Aristide; Girelli, Florian; Oriti, Daniele
2011-05-15
We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.
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.
Nuclear Quantum Gravitation and General Relativity Compared
NASA Astrophysics Data System (ADS)
Kotas, Ronald
2006-04-01
Nuclear Quantum Gravitation has 18 proofs and indications with a reasonable, non-fallacious explanation stating Gravity and Gravitation are electromagnetic and alternating, functioning in nuclei and alternating electromagnetic coupling between nuclei and other nuclei in other masses. This is according to Maxwell, Quantum, and Newtonian Laws. Nuclear Quantum Gravitation passes the Cavendish test. With the 18 proofs and indications of NQG it is clear that Gravity and Gravitation are electromagnetic and thoroughly explained by the Nuclear Quantum Gravitation theory. In comparison, General Relativity pictures mass somehow effects ``Time-Space'' about the mass, producing gravity about that mass. This is not described as an electromagnetic effect, but as a geometric function; the changing of geometry about mass. GR lists as a proof the bending of light in the area near the Sun. However, recently it was observed that the temperature of the Sun's corona is in the millions of degrees, and thus the bending of light and other electromagnetic radiation is caused by the refraction effects of the corona and heliosphere; NOT GR. The other ``proofs'' of GR are not definitive, and no one has yet explained the ``somehow'' of GR. General Relativity fails the Cavendish experiment and cannot account for the attractions between masses. It should be realized that Nuclear Quantum Gravitation provides a coherent, factual, scientific and direct physical explanation of Gravity and Gravitation thus Unifying the Physical Forces.
Csányi, V
1980-01-01
The biological, neural, cultural and technical evolutions and their phenomena have been explored, and on the basis of our findings the formation of a general theory of evolution has been undertaken. In each of the systems studied, the presence of structural building units, excitable structures and an energy-flow going through the system can be observed. Under the organizing effect of this energy-flow, the spontaneous generation of the replicative information begins and the structures of the system establish functional relations with each other. It can be demonstrated that the evolution of structures has a replicative character. The evolution goes through a phase of non-identical replication, and reaches the phase of identical replication. The parts of the system become separated, that is, compartments develop within it. The replicative information becomes compartmentalized and it converges. As a consequence of the convergence, the compartments compose new structural units which is tantamount to the development of new evolutional levels. The direction of evolution is determined by the growth of replicative information, and this process is concluded when the total system becomes one replicative unit. In the last part of the paper a few of the basic principles of evolution concerning matter, energy and information are drawn up.
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.
Universality of computation in real quantum theory
NASA Astrophysics Data System (ADS)
Belenchia, A.; D'Ariano, G. M.; Perinotti, P.
2013-10-01
Recently de la Torre et al. (Phys. Rev. Lett., 109 (2012) 090403) reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of any entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that the universality requirement would not be sufficient for the result, whereas local discriminability and the local qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a by-product we also provide a short proof of universality of C-NOT for CQT.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-01
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.
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. PMID:27091170
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.
NASA Astrophysics Data System (ADS)
Choi, Ghung G.; Li, Sheng S.
1986-07-01
A generalized theory for determining the field-enhanced thermal emission rates and carrier capture cross section of deep-level defects at very high field and for large trap density by the reverse pulsed deep-level transient spectroscopy technique has been developed in this paper. Using this new theory the field-enhanced emission rates for the DX center in a liquid-phase-epitaxial grown Sn-doped Al0.2Ga0.8As were determined for field strength up to 7×105 V/cm.
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.
NASA Astrophysics Data System (ADS)
Roy, A. K.; Chu, Shih-I.
2002-05-01
We extend the quantum hydrodynamical (QFD) formulation of time-dependent density functional theory (TDDFT) to the study of multiphoton processes of many-electron atomic systems in intense laser fields (A. K. Roy and S. I. Chu, Phys. Rev. A (in press).). The QFD-TDDFT formulation results in a single generalized nonlinear Schrodinger equation (GNLSE) and includes the many-body effects through a local time-dependent exchange-correlation (xc) potential. The GNLSE is solved by the time- dependent generalized pseudospectral method (X. M. Tong and S.I. Chu, Chem. Phys. 217) (1997) 119. (X. Chu and S. I. Chu, Phys. Rev. A 63) (2001) 023411.. The procedure is applied to the study of multiphoton ionization (MPI) and high harmonic generation (HHG) of He and Ne in intense laser fields. Four different xc energy functionals are used in the study with an aim to explore the roles of exchange and correlation ovn MPI/HHG processes in details ^1.
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.
NASA Astrophysics Data System (ADS)
Bogolyubov, N. N., Jr.; Kazaryan, A. R.; Kurbatov, A. M.; Neskoromnyi, V. N.
1987-10-01
The dynamics of a sysem of two levels radiators with a quantum electromagnetic field in the approximation of a " rotating wave" is studied . The exact Bogoliubov kynetic equation for the ful inversion and two times Greens functions for a system of radiators, in which the operators of the Bose fields do not enters explicitly, is derived by the method of exclusion of Bose-operators. Conditions are obtained, for which the irreversible relaxation of an excited system occurs by a superradiative mechanism, in the approximation of the smallness of the interaction constant, on the basis of the ideea of the scales yerarchy of the characteristic times. The relation with the superradiative experiment in impure cristals is discussed.
Solvay 1927: Quantum Theory at the Crossroads
NASA Astrophysics Data System (ADS)
Valentini, Antony
2011-04-01
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. The proceedings of the conference contain much unexpected material, and are remarkable for their clear identification of key issues that remain controversial to this day. After providing a general overview, we focus on the extensive discussions of de Broglie's pilot-wave theory, which de Broglie presented for a many-body system, including the much misunderstood critique by Pauli.
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.
Quantum information and gravity cutoff in theories with species
NASA Astrophysics Data System (ADS)
Dvali, Gia; Gomez, Cesar
2009-04-01
We show that lowering of the gravitational cutoff relative to the Planck mass, imposed by black hole physics in theories with N species, has an independent justification from quantum information theory. First, this scale marks the limiting capacity of any information processor. Secondly, by taking into the account the limitations of the quantum information storage in any system with species, the bound on the gravity cutoff becomes equivalent to the holographic bound, and this equivalence automatically implies the equality of entanglement and Bekenstein-Hawking entropies. Next, the same bound follows from quantum cloning theorem. Finally, we point out that by identifying the UV and IR threshold scales of the black hole quasi-classicality in four-dimensional field and high dimensional gravity theories, the bound translates as the correspondence between the two theories. In case when the high dimensional background is AdS, this reproduces the well-known AdS/CFT relation, but also suggests a generalization of the correspondence beyond AdS spaces. In particular, it reproduces a recently suggested duality between a four-dimensional CFT and a flat five-dimensional theory, in which gravity crosses over from four to five dimensional regime in far infrared.
Three approaches to classical thermal field theory
Gozzi, E.; Penco, R.
2011-04-15
Research Highlights: > Classical thermal field theory admits three equivalent path integral formulations. > Classical Feynman rules can be derived for all three formulations. > Quantum Feynman rules reduce to classical ones at high temperatures. > Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
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.
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.
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.
Inconstancy-theory/quantum-gravity
NASA Astrophysics Data System (ADS)
Murtaza, Faheem
1999-05-01
Inconstancy-theory is the union of "relativity" and "quantum" theories which rests upon the answers of the simple questions. 1) That if only the simple motion of a particle can not be observed without the "reference-frame" then how the whole universe can be expected to be observable without any "reference-frame". 2) Does not the inter-influence (Unity) of space-time-mass suggest that these are generated by common source and might not there be some invisible "flow" (dynamical-equilibrium) that is the cause of space-time-mass,as time itself is a flow. "Inconstancy" proposes, interalia, the principle that "relativity (generalised) is the universal law of nature in each and every respect". For that "inconstancy" admits only the light, being absolute, a real reference-frame and medium(mirror) for the display of relative "space-time-mass". Light as reference-frame in "Inconstancy" unifies "relativity" and "quantum" theories and establishes the inter-connection between "quantum-gravity" and strong-nuclear interactions, which offers the velocity of light in terms of physical and spatial-temporal components. "Inconstancy" introduces another "constant" operative in "quantum-gravity" and unveils the "graviton" location for its novel range as previously "relativity" escaped detection for v<<
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.
NASA Astrophysics Data System (ADS)
Lütkenhaus, N.; Shields, A. J.
2009-04-01
work done to date relates to point-to-point links. Another recent advance has been the development of trusted networks for QKD. This is important for further increasing the range of the technology, and for overcoming denial-of-service attacks on an individual link. It is interesting to see that the optimization of QKD devices differs for point-to-point and network applications. Network operation is essential for widespread adoption of the technology, as it can dramatically reduce the deployment costs and allow connection flexibility. Also important is the multiplexing of the quantum signals with conventional network traffic. For the future, quantum repeaters should be developed for longer range links. On the theoretical side, different approaches to security proofs have recently started to converge, offering several paradigms of the same basic idea. Our improved theoretical understanding places more stringent demands on the QKD devices. We are aware by now that finite size effects in key generation arise not only from parameter estimation. It will not be possible to generate a key from just a few hundred received signals. It is a stimulating challenge for the theory of security proofs to develop lean proof strategies that work with finite signal block sizes. As QKD advances to a real-world cryptographic solution, side channel attacks must be carefully analysed. Theoretical security proofs for QKD schemes are so far based on physical models of these devices. It is in the nature of models that any real implementation will deviate from this model, creating a potential weakness for an eavesdropper to exploit. There are two solutions to this problem: the traditional path of refining the models to reduce the deviations, or the radically different approach of device-independent security proofs, in which none or only a few well controlled assumptions about the devices are made. Clearly, it is desirable to find security proofs that require only minimal or fairly general model
Borzou, Ahmad; Lin, Kai; Wang, Anzhong E-mail: k_lin@baylor.edu
2012-02-01
In this paper, we study electromeganetic static spacetimes in the nonrelativisitc general covariant theory of the Hořava-Lifshitz (HL) gravity, proposed recently by Hořava and Melby-Thompson, and present all the electric static solutions, which represent the generalization of the Reissner-Nordström solution found in Einstein's general relativity (GR). The global/local structures of spacetimes in the HL theory in general are different from those given in GR, because the dispersion relations of test particles now contain high-order momentum terms, so the speeds of these particles are unbounded in the ultraviolet (UV). As a result, the conception of light-cones defined in GR becomes invalid and test particles do not follow geodesics. To study black holes in the HL theory, we adopt the geometrical optical approximations, and define a horizon as a (two-closed) surface that is free of spacetime singularities and on which massless test particles are infinitely redshifted. With such a definition, we show that some of our solutions give rise to (charged) black holes, although the radii of their horizons in general depend on the energies of the test particles.
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.
Quantum Ontology in the Light of Gauge Theories
NASA Astrophysics Data System (ADS)
Catren, Gabriel
2014-03-01
By using the conceptual framework provided by the theory of constrained Hamiltonian systems, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations to the observables of unconstrained Hamiltonian systems. The quantum postulate establishes a faithful correspondence between the observables that allow us to identify the states and the operators that act on these states. According to this quantum ontology, quantum states provide a complete description of all the objective properties of quantum systems.
Finite temperature quantum fields in expanding universes
NASA Astrophysics Data System (ADS)
Hu, B. L.
1982-01-01
The thermodynamics of an ideal relativistic quantum gas in expansion is studied. It is found that only for conformally invariant fields in conformally static spacetime can thermal equilibrium be strictly maintained. A finite temperature theory can be defined under the condition of quasi equilibrium when the background expansion is nearly adiabatic. The high temperature expansion of the energy density for massive nonconformal fields in Robertson-Walker universes and for conformal fields in Bianchi Type-I universes are calculated. The importance of these results on phase transition and quantum processes in the early universe is discussed.
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.
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.
Theory of NMR 1 /T1 relaxation in a quantum spin nematic in an applied magnetic field
NASA Astrophysics Data System (ADS)
Smerald, Andrew; Shannon, Nic
2016-05-01
There is now strong theoretical evidence that a wide range of frustrated magnets should support quantum spin-nematic order in an applied magnetic field. Nonetheless, the fact that spin-nematic order does not break time-reversal symmetry makes it very difficult to detect in experiment. In this article, we continue the theme begun in Phys. Rev. B 88, 184430 (2013), 10.1103/PhysRevB.88.184430, of exploring how spin-nematic order reveals itself in the spectrum of spin excitations. Building on an earlier analysis of inelastic neutron scattering [Phys. Rev. B 91, 174402 (2015), 10.1103/PhysRevB.91.174402], we show how the NMR 1 /T1 relaxation rate could be used to identify a spin-nematic state in an applied magnetic field. We emphasize the characteristic universal features of 1 /T1 using a symmetry-based description of the spin-nematic order parameter and its fluctuations. Turning to the specific case of spin-1/2 frustrated ferromagnets, we show that the signal from competing spin-wave excitations can be suppressed through a judicious choice of nuclear site and field direction. As a worked example, we show how 31P NMR in the square lattice frustrated ferromagnet BaCdVO (PO4)2 is sensitive to spin-nematic order.
Hybrid quantum computing: semicloning for general database retrieval
NASA Astrophysics Data System (ADS)
Lanzagorta, Marco; Uhlmann, Jeffrey K.
2005-05-01
Quantum computing (QC) has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing (CC). In particular, QC is able to exploit the special properties of quantum superposition to achieve computational parallelism beyond what can be achieved with parallel CC computers. However, these special properties are not applicable for general computation. Therefore, we propose the use of "hybrid quantum computers" (HQCs) that combine both classical and quantum computing architectures in order to leverage the benefits of both. We demonstrate how an HQC can exploit quantum search to support general database operations more efficiently than is possible with CC. Our solution is based on new quantum results that are of independent significance to the field of quantum computing. More specifically, we demonstrate that the most restrictive implications of the quantum No-Cloning Theorem can be avoided through the use of semiclones.
Quantum chromodynamics in background fields
NASA Astrophysics Data System (ADS)
Huang, Tao; Huang, Zheng
1989-02-01
We try to build a framework for quantum chromodynamics in background fields. The nonvanishing vacuum condensates are described by the classical fields, while the corresponding quantum fields are quantized in the Furry representation and the physical states are defined in the physical QCD vacuum. The complete quark and gluon propagators are discussed in this framework and running condensate parameters are introduced by the renormalization requirement. A modified Callan-Symanzik equation is derived by taking account of the nonperturbative corrections.
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.
NASA Astrophysics Data System (ADS)
Tanatar, B.; Bulutay, C.
1999-06-01
Dynamic local-field correction (LFC) brings a richer picture about the description of a many-body system than the standard mean-field theories. Here we investigate the ground-state properties of a quasi-one-dimensional electronic system using the quantum version of the Singwi-Tosi-Land-Sjölander (STLS) theory and present a critical account of its performance. The results are markedly different than those theories based on static LFC and the random-phase approximation; an example is the static structure factor, which develops a significant peak at low densities, signaling a developing ordered phase. An indication of growing instability at low densities is seen on G(q,0), the static behavior of the dynamic LFC, which has an oscillatory character with a magnitude exceeding unity, peaking exactly at 4kF. The pair-correlation function comes out as positive for the densities considered in this work. The correlation energy and the compressibility curves are seen to be quite close to the static STLS results. A flaw of the theory is the significantly negative values of the dynamic structure factor around the plasmon frequencies, also the lifetime of the plasmons turns out to be negative away from the single-pair continuum. In summary, the major shortcomings of the dynamic STLS scheme are the violation of the compressibility sum rule (as in the static STLS case) and the misrepresentation of the plasmons in the dynamic structure factor.
‘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.
Quantum rotor theory of systems of spin-2 bosons
NASA Astrophysics Data System (ADS)
Payrits, Matjaž; Barnett, Ryan
2016-08-01
We consider quantum phases of tightly confined spin-2 bosons in an external field under the presence of rotationally invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean field ground-state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order by disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial-mode problem with finite-particle number, it is known that, due to symmetry-restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework, we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave-function overlaps, we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this, we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case, we do find the phenomenon of order by disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.
From Entropic Dynamics to Quantum Theory
Caticha, Ariel
2009-12-08
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting theory resembles both Nelson's stochastic mechanics and general relativity. The statistical manifold is a dynamical entity: its geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. There is a new quantum version of the equivalence principle: 'osmotic' mass equals inertial mass. Mass and the phase of the wave function are explained as features of purely statistical origin.
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.
Gravity and Quantum Theory Unified
NASA Astrophysics Data System (ADS)
Warren, Gary
Historic arguments against Aether theories disappear if the Aether is a 4D compressible hyperfluid in which each particle is our observation of a hypervortex, formed in and comprised of hyperfluid. Such Aether resolves ``spooky action at a distance'' which allows unification of gravity and quantum theory. Light is transverse waves in free space (away from hypervortices) in the hyperfluid. Their detailed behavior is why we observe a curved 3D Lorentz universe - a slice through the 4D hyperverse. Meanwhile, detailed hypervortex behavior, including faster-than-light longitudinal waves in and along hypervortices, explain quantum phenomena. A particular Lagrangian for such a hyperfluid regenerates Maxwell's equations, plus an equation for gravity, and an equation for electric charge. Couplings among these equations generate a discrete spectrum of hypervortex solutions that we observe as a spectrum of particles. Gravity results from gradients in the fluid density near vortices. Observed clock rates depend on fluid density, and vortex motion thus intertwining gravity, clock rates and quantum phenomena. Implied experiments will be discussed.
Quantum theory allows for absolute maximal contextuality
NASA Astrophysics Data System (ADS)
Amaral, Barbara; Cunha, Marcelo Terra; Cabello, Adán
2015-12-01
Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum S of n probabilities, and the independence number α and the Tsirelson-like number ϑ of the corresponding exclusivity graph are, respectively, the maximum of S for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which ϑ /α approaches n . Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost-absolute-maximal contextuality.
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.
Ramanantoanina, Harry; Urland, Werner; Cimpoesu, Fanica; Daul, Claude
2013-09-01
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.
NASA Astrophysics Data System (ADS)
Glinka, L. A.
2009-01-01
Global One-Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3 + 1 metric, where the dimension is a volume of threedimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3 + 1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose-Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. It confirm that the proposed Quantum Gravity toy model has well-defined classical limit in accordance with classical gravity theory.
Efficient perturbation theory for quantum lattice models.
Hafermann, H; Li, G; Rubtsov, A N; Katsnelson, M I; Lichtenstein, A I; Monien, H
2009-05-22
We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.
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.
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
Entanglement and thermodynamics in general probabilistic theories
NASA Astrophysics Data System (ADS)
Chiribella, Giulio; Scandolo, Carlo Maria
2015-10-01
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement. The correspondence is then used to define entanglement measures in the general probabilistic framework. Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).
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…
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).
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.
Generalized Heisenberg theory of turbulence
NASA Technical Reports Server (NTRS)
Uberoi, M. S.; Narain, J. P.
1974-01-01
Solutions of the generalized theory are obtained which are consistent with the previous work on energy transfer measurements. They also agree with the measurements of turbulent energy spectrum for wave numbers in the universal equilibrium range.
Quantum gauge theories from geometry
NASA Astrophysics Data System (ADS)
Galehouse, Daniel C.
2006-03-01
Geometrical theories have been developed to describe quantum interacting particles with full mathematical covariance. They possess a sophisticated gauge structure that derives from the fundamental properties of the geometry. These theories are all implicitly quantized and come in three known types: Weyl, non-compactified Kaluza-Klein, and, as presented here, Dirac. The spin one-half particle is a conformal wave in an eight dimensional Riemannian space. The coordinates transform locally as spinors and project into space time to give the known gravitational and electromagnetic forces. The gauge structure of the weak interactions appears as well, as in this space the electron transforms into a neutrino under hyper-rotations. The possibility of including the strong interactions and the corresponding gauge system is discussed.
Generalized Clustered Quantum Hall States
NASA Astrophysics Data System (ADS)
Simon, Steven H.; Cooper, Nigel R.; Rezayi, Ed
2005-03-01
The Read-Rezayi (parafermion) quantum Hall states[1] for bosons can be defined as states where the wavefunction does not vanish when g bosons come together to the same point, but does vanish as z^2 as a g+1st particle approaches that point. These states can equivalently be defined as the unique ground state of a point contact g+1 particle interaction Hamiltonian. Interestingly, the series of Read-Rezayi states appears to describe well the groundstates of rotating Bose condensates with point-contact two body interactions at a series of filling fractions [2]. If one attaches a Jastrow factor to such bose wavefunctions, one obtains fermion wavefunctions that may occur in electronic quantum Hall systems including the (g=2) Pfaffian [3] and the (g=3) ν=13/5 Read-Rezayi state [1]. In this work, we consider generalized cluster wavefunctions defined by the algebraic manner in which a wavefunction vanishes as g+1 particles coalesce. We find Hamiltonians that generate these wavefunctions as their exact ground state. Among this series of states is the previously studied Haffnian wavefunction[4] and a host of states not previously discussed. We catalogue and study the new states and discuss whether any of them might occur in actual physical systems. [1] N. Read and E. Rezayi, PRB59, 8084 (1999). [2] N. R. Cooper, N. K. Wilkin, and J. M. F. Gunn, PRL87, 120405 (2001) [3] G. Moore and N. Read, Nuc. Phys. B360, 362 (1991). [4] D. Green, PhD Thesis.
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.
Quantum mechanical model in gravity theory
NASA Astrophysics Data System (ADS)
Losyakov, V. V.
2016-05-01
We consider a model of a real massive scalar field defined as homogeneous on a d-dimensional sphere such that the sphere radius, time scale, and scalar field are related by the equations of the general theory of relativity. We quantize this system with three degrees of freedom, define the observables, and find dynamical mean values of observables in the regime where the scalar field mass is much less than the Planck mass.
General Quantum Interference Principle and Duality Computer
NASA Astrophysics Data System (ADS)
Long, Gui-Lu
2006-05-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
Quantum theory of Manakov solitons
Rand, Darren; Prucnal, Paul R.; Steiglitz, Ken
2005-05-15
A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schroedinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.
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
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).
Variational Methods for Field Theories.
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
The thesis has four parts, dealing with four 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. This includes a better quantitative agreement for the string tensions in the two approaches. In the second part, we use free field theory as a loboratory for a new variational blocking-tuncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes(Born-Oppenheimer approximation). This "adiabatic truncation" method gives very accurate results for ground -state energy density and correlation functions. Without the adiabatic method, a much larger number of state per block must be kept to get comparable results. 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 Eclidean 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. This transition is a rudimentary version of the actual transition known to occur in the XY model, and is
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Entanglement of Low-Energy Excitations in Conformal Field Theory
Alcaraz, Francisco Castilho; Ibanez Berganza, Miguel; Sierra, German
2011-05-20
In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.
Some Properties of Generalized Connections in Quantum Gravity
NASA Astrophysics Data System (ADS)
Velhinho, J. M.
2002-12-01
Theories of connections play an important role in fundamental interactions, including Yang-Mills theories and gravity in the Ashtekar formulation. Typically in such cases, the classical configuration space {A}/ {G} of connections modulo gauge transformations is an infinite dimensional non-linear space of great complexity. Having in mind a rigorous quantization procedure, methods of functional calculus in an extension of {A}/ {G} have been developed. For a compact gauge group G, the compact space /line { {A}{ {/}} {G}} ( ⊃ {A}/ {G}) introduced by Ashtekar and Isham using C*-algebraic methods is a natural candidate to replace {A}/ {G} in the quantum context, 1 allowing the construction of diffeomorphism invariant measures. 2,3,4 Equally important is the space of generalized connections bar {A} introduced in a similar way by Baez. 5 bar {A} is particularly useful for the definition of vector fields in /line { {A}{ {/}} {G}} , fundamental in the construction of quantum observables. 6 These works crucially depend on the use of (generalized) Wilson variables associated to certain types of curves. We will consider the case of piecewise analytic curves, 1,2,5 althought most of the arguments apply equally to the piecewise smooth case. 7,8...
Generalized uncertainty principle in Bianchi type I quantum cosmology
NASA Astrophysics Data System (ADS)
Vakili, B.; Sepangi, H. R.
2007-07-01
We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.
Quantum physics reimagined for the general public
NASA Astrophysics Data System (ADS)
Bobroff, Julien
2015-03-01
Quantum Physics has always been a challenging issue for outreach. It is invisible, non-intuitive and written in sophisticated mathematics. In our ``Physics Reimagined'' research group, we explore new ways to present that field to the general public. Our approach is to develop close collaborations between physicists and designers or graphic artists. By developing this new kind of dialogue, we seek to find new ways to present complex phenomena and recent research topics to the public at large. For example, we created with web-illustrators a series of 3D animations about basic quantum laws and research topics (graphene, Bose-Einstein condensation, decoherence, pump-probe techniques, ARPES...). We collaborated with designers to develop original setups, from quantum wave animated models or foldings to a superconducting circus with levitating animals. With illustrators, we produced exhibits, comic strips or postcards displaying the physicists in their labs, either famous ones or even our own colleagues in their daily life as researchers. With artists, we recently made a stop-motion picture to explain in an esthetic way the process of discovery and scientific publication. We will discuss how these new types of outreach projects allowed us to engage the public with modern physics both on a scientific and cultural level and how the concepts and process can easily be replicated and expanded by other physicists. We are at the precise time when creative tools, interfaces, and ways of sharing and learning are rapidly evolving (wikipedia, MOOCs, smartphones...). If scientists don't step forward to employ these tools and develop new resources, other people will, and the integrity of the science and underlying character of research risks being compromised. All our productions are free to use and can be downloaded at www.PhysicsReimagined.com (for 3D quantum videos, specific link: www.QuantumMadeSimple.com) This work benefited from the support of the Chair ``Physics Reimagined
Uncertainty relation revisited from quantum estimation theory
Watanabe, Yu; Sagawa, Takahiro; Ueda, Masahito
2011-10-15
We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.
Generalized eikonal approximation for strong-field ionization
NASA Astrophysics Data System (ADS)
Cajiao Vélez, F.; Krajewska, K.; Kamiński, J. Z.
2015-05-01
We develop the eikonal perturbation theory to describe the strong-field ionization by finite laser pulses. This approach in the first order with respect to the binding potential (the so-called generalized eikonal approximation) avoids a singularity at the potential center. Thus, in contrast to the ordinary eikonal approximation, it allows one to treat rescattering phenomena in terms of quantum trajectories. We demonstrate how the first Born approximation and its domain of validity follow from eikonal perturbation theory. Using this approach, we study the coherent interference patterns in photoelectron energy spectra and their modifications induced by the interaction of photoelectrons with the atomic potential. Along with these first results, we discuss the prospects of using the generalized eikonal approximation to study strong-field ionization from multicentered atomic systems and to study other strong-field phenomena.
On classical and quantum dynamics of tachyon-like fields and their cosmological implications
Dimitrijević, Dragoljub D. Djordjević, Goran S. Milošević, Milan; Vulcanov, Dumitru
2014-11-24
We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking for a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.
NASA Astrophysics Data System (ADS)
Ruggenthaler, Michael; Flick, Johannes; Pellegrini, Camilla; Appel, Heiko; Tokatly, Ilya V.; Rubio, Angel
2014-07-01
In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the density-functional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.
Multichannel quantum defect theory for polar molecules
NASA Astrophysics Data System (ADS)
Elfimov, Sergei V.; Dorofeev, Dmitrii L.; Zon, Boris A.
2014-02-01
Our work is devoted to developing a general approach for nonpenetrating Rydberg states of polar molecules. We propose a method to estimate the accuracy of calculation of their wave functions and quantum defects. Basing on this method we estimate the accuracy of Born-Oppenheimer (BO) and inverse Born-Oppenheimer (IBO) approximations for these states. This estimation enables us to determine the space and energy regions where BO and IBO approximations are valid. It depends on the interplay between l coupling (due to dipole potential of the core) and l uncoupling (due to rotation the core). Next we consider the intermediate region where both BO and IBO are not valid. For this intermediate region we propose a modification of Fano's multichannel quantum defect theory to match BO and IBO wave functions and show that it gives more reliable results. They are demonstrated on the example of SO molecule.
Iengo, R. |; Jug, G. |
1995-09-01
We investigate the phenomenon of the decay of a supercurrent through homogeneous nucleation of vortex-antivortex pairs in a two-dimensional (2D) like superconductor or superfluid by means of a quantum electrodynamic formulation for the decay of the 2D vacuum. The case in which both externally driven current and Magnus force are present is treated exactly, taking the vortex activation energy and its inertial mass as independent parameters. Quantum dissipation is included through the formulation introduced by Caldeira and Leggett. The most relevant consequence of quantum dissipation is the elimination of the threshold for vortex production due to the Magnus force. In the dissipation-dominated case, corresponding formally to the limit of zero intertial mass, an exact formula for the pair production rate is given. If however the inertial mass is strictly zero we find that vortex production is inhibited by a quantum effect related to the Magnus force. The possibility of including vortex pinning is investigated by means of an effective harmonic potential. While an additional term in the vortex activation energy can account for the effect of a finite barrier in the direction perpendicular to the current, pinning along the current depresses the role of the Magnus force in the dissipation-dominated dynamics, except for the above-mentioned quantum effect. A possible description of vortex nucleation due to the combined effects of temperature and externally driven currents is also presented along with an evaluation of the resulting voltage drop.
Clustering properties, Jack polynomials and unitary conformal field theories
NASA Astrophysics Data System (ADS)
Estienne, Benoit; Regnault, Nicolas; Santachiara, Raoul
2010-01-01
Recently, Jack polynomials have been proposed as natural generalizations of Z Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A. These theories can be considered as non-unitary solutions of a more general series of CFTs with Z symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.
Generalized Yang-Mills theory and gravity
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming
2016-02-01
We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories, in general, include a graviton, a dilaton and a rank-two antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via Bern-Carrasco-Johansson duality can be made more manifest in this formulation.
NASA Astrophysics Data System (ADS)
Golden, Sidney
1995-02-01
As characterized experimentally by Rutherford, an essential feature of radioactive decompositions is their being constituted of randomly occurring events in terms of which the decomposing systems exhibit exponential temporal decay behavior with associated characteristic half-lives. This feature is rigorously accounted for generally by the recent temporally-quantized dynamical theory of strictly-irreversible evolution of isolated and localized non-relativistic quantum systems, which theory also obviates the celebrated Zeno's paradox of conventional quantum theory.
Whiteheadian process and quantum theory
Stapp, H.
1998-08-01
There are deep similarities between Whitehead's idea of the process by which nature unfolds and the ideas of quantum theory. Whitehead says that the world is made of ''actual occasions'', each of which arises from potentialities created by prior actual occasions. These actual occasions are happenings modeled on experiential events, each of which comes into being and then perishes, only to be replaced by a successor. It is these experience-like happenings that are the basic realities of nature, according to Whitehead, not the persisting physical particles that Newtonian physics took be the basic entities. Similarly, Heisenberg says that what is really happening in a quantum process is the emergence of an actual from potentialities created by prior actualities. In the orthodox Copenhagen interpretation of quantum theory the actual things to which the theory refer are increments in ''our knowledge''. These increments are experiential events. The particles of classical physics lose their fundamental status: they dissolve into diffuse clouds of possibilities. At each stage of the unfolding of nature the complete cloud of possibilities acts like the potentiality for the occurrence of a next increment in knowledge, whose occurrence can radically change the cloud of possibilities/potentialities for the still-later increments in knowledge. The fundamental difference between these ideas about nature and the classical ideas that reigned from the time of Newton until this century concerns the status of the experiential aspects of nature. These are things such as thoughts, ideas, feelings, and sensations. They are distinguished from the physical aspects of nature, which are described in terms of quantities explicitly located in tiny regions of space and time. According to the ideas of classical physics the physical world is made up exclusively of things of this latter type, and the unfolding of the physical world is determined by causal connections involving only these things
Problems of Quantum Theory may be Solved by an Emulation Theory of Quantum Physics
NASA Astrophysics Data System (ADS)
Woesler, Richard
2005-02-01
The emulation interpretation of quantum theory is described which may solve problems of the Copenhagen interpretation finally. According to Kolmogorov complexity theory it is conceivable that a bit string exists encoding our world which can be computed by an appropriate generalized Turing machine. In this case the computation would emulate the world, therefore this can be called an emulation theory of quantum physics, and the emulation interpretation of quantum theory. The probability of a string is dominated by the probabilities of its shortest programs which is known as the `coding theorem'. This leads to the suggestion that there may be a relatively short shortest program by which our world may be run. This suggestion appears to be in accordance with our world. The world exhibits a number of symmetries. It is plausible that the shortest algorithm for our special world is shorter than those for worlds where symmetries are broken more often than in our world, because each further deviation from a symmetry has to be encoded within the algorithm which would enlarge its length. Therefore, laws of physics may be identical rather globally in spacetime. Further, in the Copenhagen interpretation of quantum theory it is defined, how to compute probabilities for, e.g., measurement results when conducting measurements on variables of quantum systems. In a completely satisfactory theory of everything this would not be sufficient, but such a theory should give a reason why the values of the probabilities seem, as far as it is known, to be identical also in all different regions of the observed world. The emulation interpretation suggests that all deviations from this symmetry of the probabilities would enlarge the shortest program of the world, and, therefore, we would probably not live in a world with such deviations. A second question arises from the attempt to combine the theory of black holes, thermodynamics and quantum theory. Bekenstein derives a holography principle
Relational quadrilateralland II: The Quantum Theory
NASA Astrophysics Data System (ADS)
Anderson, Edward; Kneller, Sophie
2014-04-01
We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.
Generalized contexts and consistent histories in quantum mechanics
Losada, Marcelo; Laura, Roberto
2014-05-15
We analyze a restriction of the theory of consistent histories by imposing that a valid description of a physical system must include quantum histories which satisfy the consistency conditions for all states. We prove that these conditions are equivalent to imposing the compatibility conditions of our formalism of generalized contexts. Moreover, we show that the theory of consistent histories with the consistency conditions for all states and the formalism of generalized context are equally useful representing expressions which involve properties at different times.
Generalized contexts and consistent histories in quantum mechanics
NASA Astrophysics Data System (ADS)
Losada, Marcelo; Laura, Roberto
2014-05-01
We analyze a restriction of the theory of consistent histories by imposing that a valid description of a physical system must include quantum histories which satisfy the consistency conditions for all states. We prove that these conditions are equivalent to imposing the compatibility conditions of our formalism of generalized contexts. Moreover, we show that the theory of consistent histories with the consistency conditions for all states and the formalism of generalized context are equally useful representing expressions which involve properties at different times.
Reversible Framework for Quantum Resource Theories.
Brandão, Fernando G S L; Gour, Gilad
2015-08-14
In recent years it has been recognized that properties of physical systems such as entanglement, athermality, and asymmetry, can be viewed as resources for important tasks in quantum information, thermodynamics, and other areas of physics. This recognition was followed by the development of specific quantum resource theories (QRTs), such as entanglement theory, determining how quantum states that cannot be prepared under certain restrictions may be manipulated and used to circumvent the restrictions. Here we discuss the general structure of QRTs, and show that under a few assumptions (such as convexity of the set of free states), a QRT is asymptotically reversible if its set of allowed operations is maximal, that is, if the allowed operations are the set of all operations that do not generate (asymptotically) a resource. In this case, the asymptotic conversion rate is given in terms of the regularized relative entropy of a resource which is the unique measure or quantifier of the resource in the asymptotic limit of many copies of the state. This measure also equals the smoothed version of the logarithmic robustness of the resource.