NASA Astrophysics Data System (ADS)
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
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.
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.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Reverse engineering quantum field theory
NASA Astrophysics Data System (ADS)
Oeckl, Robert
2012-12-01
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
Lectures on Matrix Field Theory
NASA Astrophysics Data System (ADS)
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
Kirby S. Chapman; Sarah R. Nuss-Warren
2007-02-01
The objective of this project is to identify, develop, test, and commercialize emissions control and monitoring technologies that can be implemented by exploration and production (E&P) operators to significantly lower the cost of environmental compliance and expedite project permitting. The project team takes considerable advantage of the emissions control research and development efforts and practices that have been underway in the gas pipeline industry for the last 12 years. These efforts and practices are expected to closely interface with the E&P industry to develop cost-effective options that apply to widely-used field and gathering engines, and which can be readily commercialized. The project is separated into two phases. Phase 1 work establishes an E&P industry liaison group, develops a frequency distribution of installed E&P field engines, and identifies and assesses commercially available and emerging engine emissions control and monitoring technologies. Current and expected E&P engine emissions and monitoring requirements are reviewed, and priority technologies are identified for further development. The identified promising technologies are tested on a laboratory engine to confirm their generic viability. In addition, a full-scale field test of prototype emissions controls will be conducted on at least ten representative field engine models with challenging emissions profiles. Emissions monitoring systems that are integrated with existing controls packages will be developed. Technology transfer/commercialization is expected to be implemented through compressor fleet leasing operators, engine component suppliers, the industry liaison group, and the Petroleum Technology Transfer Council. This topical report discusses work completed during Phase 1 of the project Cost Effective Reciprocating Engine Emissions Control and Monitoring for E&P Field and Gathering Engines. In this report information, data, and results are compiled and summarized from quarterly
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Computational quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, Rainer
2006-05-01
I will give an overview on recent attempts to solve the time-dependent Dirac equation for the electron-positron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electron-positron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pair-production due to the supercriticality of the potential together with the scattering at the barrier involving the Pauli-principle. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
Quantum 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.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
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.
Quantum Field Theory, Revised Edition
NASA Astrophysics Data System (ADS)
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
NASA Astrophysics Data System (ADS)
Maxfield, Travis; Robbins, Daniel; Sethi, Savdeep
2016-11-01
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2, 0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
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.
Study of Low Temperature Baking Effect on Field Emission on Nb Samples Treated by BEP, EP, and BCP
Andy Wu, Song Jin, Robert Rimmer, Xiang Yang Lu, K. Zhao, Laura MacIntyre, Robert Ike
2010-05-01
Field emission is still one of the major obstacles facing Nb superconducting radio frequency (SRF) community for allowing Nb SRF cavities to reach routinely accelerating gradient of 35 MV/m that is required for the international linear collider. Nowadays, the well know low temperature backing at 120 oC for 48 hours is a common procedure used in the SRF community to improve the high field Q slope. However, some cavity production data have showed that the low temperature baking may induce field emission for cavities treated by EP. On the other hand, an earlier study of field emission on Nb flat samples treated by BCP showed an opposite conclusion. In this presentation, the preliminary measurements of Nb flat samples treated by BEP, EP, and BCP via our unique home-made scanning field emission microscope before and after the low temperature baking are reported. Some correlations between surface smoothness and the number of the observed field emitters were found. The observed experimental results can be understood, at least partially, by a simple model that involves the change of the thickness of the pent-oxide layer on Nb surfaces.
String theory in electromagnetic fields
NASA Astrophysics Data System (ADS)
Ambjørn, Jan; Makeenko, Yuri M.; Semenoff, Gordon W.; Szabo, Richard J.
2003-02-01
A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature formalism and Hagedorn behaviour in external fields, Debye screening, D-brane scattering, thermodynamics of D-branes, and noncommutative field and string theories on D-branes. The electric field instabilities are emphasized throughout and contrasted with the case of magnetic fields. A new derivation of the velocity-dependent potential between moving D-branes is presented, as is a new result for the velocity corrections to the one-loop thermal effective potential.
On supersymmetric Lifshitz field theories
NASA Astrophysics Data System (ADS)
Chapman, Shira; Oz, Yaron; Raviv-Moshe, Avia
2015-10-01
We consider field theories that exhibit a supersymmetric Lifshitz scaling with two real supercharges. The theories can be formulated in the language of stochastic quan-tization. We construct the free field supersymmetry algebra with rotation singlet fermions for an even dynamical exponent z = 2 k in an arbitrary dimension. We analyze the classical and quantum z = 2 supersymmetric interactions in 2 + 1 and 3 + 1 spacetime dimensions and reveal a supersymmetry preserving quantum diagrammatic cancellation. Stochastic quantization indicates that Lifshitz scale invariance is broken in the (3 + 1)-dimensional quantum theory.
NASA Astrophysics Data System (ADS)
Weinberg, Steven
1996-08-01
In this second volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly expoistion of quantum theory. Volume 2 provides an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Exercises are included at the end of each chapter.
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.
Intracardiac electrophysiology study (EPS)
... rhythms - EPS; Bradycardia - EPS; Tachycardia - EPS; Fibrillation - EPS; Arrhythmia - EPS; Heart block - EPS ... you have signs of an abnormal heart rhythm ( arrhythmia ). You may need to have other tests before ...
Field-theory methods in coagulation theory
Lushnikov, A. A.
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Lectures on Crystal Field Theory
1982-11-01
used to calculate the electric dipole transition probabilities using the theory of Judd (1962) and Ofelt (1962)o As of 1970, all these objectives had...metry higher than C1 or C•. (4) The calculation of transltion probabilities, Zeeman splitting factors, Judd - Ofelt intensity parameters, branching ratios...INTERACTIONS ..................................... 37 4.1 Phenomenological Theory of Crystal Fields ................ 37 4.1.1 Matrix Elements of H in J States
Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F
2015-02-10
We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.
Unitarity of superstring field theory
NASA Astrophysics Data System (ADS)
Sen, Ashoke
2016-12-01
We complete the proof of unitarity of (compactified) heterotic and type II string field theories by showing that in the cut diagrams only physical states appear in the sum over intermediate states. This analysis takes into account the effect of mass and wave-function renormalization, and the possibility that the true vacuum may be related to the perturbative vacuum by small shifts in the string fields.
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.
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.
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.
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.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro E-mail: mwhite@berkeley.edu
2015-09-01
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
NASA Astrophysics Data System (ADS)
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
HBT-EP Program: MHD Dynamics and Active Control through 3D Fields and Currents
NASA Astrophysics Data System (ADS)
Navratil, G. A.; Abler, M. C.; Bialek, J.; Brooks, J. W.; Byrne, P. J.; Desanto, S.; Hughes, P. E.; Levesque, J. P.; Mauel, M. E.; Rhodes, D. J.; Hansen, C. J.
2016-10-01
The HBT-EP active mode control research program aims to: (i) advance understanding of the effects of 3D shaping on advanced tokamak fusion performance, (ii) resolve important MHD issues associated with disruptions, and (iii) measure and mitigate the effects of 3D scrape-off layer (SOL) currents through active and passive control of the plasma edge and conducting boundary structures. A GPU-based low latency control system uses 96 inputs and 64 outputs to control the plasma boundary. An in-vessel adjustable ferritic wall is used to study ferritic RWMs with increased growth rates, RMP response, and disruptivity. A quasi-linear sharp-boundary model is developed to study effects of toroidal curvature and plasma shaping on beta limits with resistive plasmas and walls. Measurement of currents between vessel sections reveals currents running from the plasma to the wall during wall-touching kink modes and disruptions. Asymmetries in plasma current are observed using segmented Rogowski coils. Biased electrodes in the plasma are used to control rotation of external kinks and drive currents in the SOL. An extensive array of SOL current monitors and edge drive electrodes will be installed for pioneering studies of helical edge current control. Supported by U.S. DOE Grant DE-FG02-86ER53222.
Changing Views of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2010-03-01
The first part of this talk reviews changes in our views regarding quantum field theory since its beginnings, leading eventually to the modern view that our most successful field theories may in fact be effective field theories, valid only as low energy approximations to an underlying theory that may not be a field theory at all. In the second part, I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory, and finally cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe. The second part is substantially the same as a talk given a month earlier at the 6th International Workshop on Chiral Dynamics, at the University of Bern, which is reproduced here.
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
Field Analysis and Potential Theory
1985-06-01
distance measured from a point singularity P, then the total source strength associated with a neighbourhood of P remains finite if foIt’ n is bounded...a neighbourhood of the source, where it takes the form ii 296 FIELD ANALYSIS AND POTENTIAL THEORY [Sec.4.11 T- 1k + U where r’ is distance measured ...8217,t) + f2(x~yzt) in a neighbourhood of the point P, where r’ is distance measured from P and fj and f 2 are well-behaved functions of space and time
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
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.
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki
2010-01-15
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Field Theory of Fundamental Interactions
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2017-01-01
First, we present two basic principles, the principle of interaction dynamics (PID) and the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action under energy-momentum conservation constraint. We show that the PID is the requirement of the presence of dark matter and dark energy, the Higgs field and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). It is clear that PRI is the logic requirement of any gauge theory. With PRI, we demonstrate that the coupling constants for the strong and the weak interactions are the main sources of these two interactions, reminiscent of the electric charge. Second, we emphasize that symmetry principles-the principle of general relativity and the principle of Lorentz invariance and gauge invariance-together with the simplicity of laws of nature, dictate the actions for the four fundamental interactions. Finally, we show that the PID and the PRI, together with the symmetry principles give rise to a unified field model for the fundamental interactions, which is consistent with current experimental observations and offers some new physical predictions. The research is supported in part by the National Science Foundation (NSF) grant DMS-1515024, and by the Office of Naval Research (ONR) grant N00014-15-1-2662.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Supersymmetric extensions of K field theories
NASA Astrophysics Data System (ADS)
Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.
2012-02-01
We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.
Kirby S. Chapman; Sarah R. Nuss-Warren
2006-12-31
This report highlights work done on a project intended to lower the cost of environmental compliance and expedite project permitting for Exploration and Production (E&P) operators by identifying, developing, testing, and commercializing emissions control and monitoring technologies. Promising technologies have already been identified and developed. Current work focuses on testing these promising technologies. Specifically, several technologies are being tested in the laboratory for application to lean-burn engines or fully characterized on-site for use with rich-burn engines. Upon completion of these tests, the most cost-effective and robust technologies will be tested in the field and commercialization will ensue. During this quarter, progress in laboratory testing for lean-burn engines was limited by maintenance issues on the KSU Ajax DP-115. The difficulties that required maintenance to be performed will likely require that the 180 psig prototype valve be tested in the future, if possible. The maintenance was performed, and it is expected that the Ajax will be available for testing in the coming quarter. Although laboratory testing was slowed as a result of maintenance issues, progress in experimental characterization of technologies has been significant. NSCR systems will be characterized as applied to rich-burn engines on-site. This characterization will ensure high-quality data in final field testing on rich-burn engines and is considered to be essential, despite that the work requires the delay of official field testing until 2008. Many preliminary and administrative tasks have been completed, including initial site selection, official proposal submittal, and beginning a process to approve necessary changes to installed field engines.
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.
Keith Hohn; Sarah R. Nuss-Warren
2011-08-31
This final report describes a project intended to identify, develop, test, and commercialize emissions control and monitoring technologies that can be implemented by E&P operators to significantly lower their cost of environmental compliance and expedite project permitting. Technologies were installed and tested in controlled laboratory situations and then installed and tested on field engines based on the recommendations of an industry-based steering committee, analysis of installed horsepower, analysis of available emissions control and monitoring technologies, and review of technology and market gaps. The industry-recognized solution for lean-burn engines, a low-emissions-retrofit including increased airflow and pre-combustion chambers, was found to successfully control engine emissions of oxides of nitrogen (NO{sub X}) and carbon monoxide (CO). However, the standard non-selective catalytic reduction (NSCR) system recognized by the industry was found to be unable to consistently control both NO{sub X} and CO emissions. The standard NSCR system was observed to produce emissions levels that changed dramatically on a day-to-day or even hour-to-hour basis. Because difficulties with this system seemed to be the result of exhaust gas oxygen (EGO) sensors that produced identical output for very different exhaust gas conditions, models were developed to describe the behavior of the EGO sensor and an alternative, the universal exhaust gas oxygen (UEGO) sensor. Meanwhile, an integrated NSCR system using an advanced, signal-conditioned UEGO sensor was tested and found to control both NO{sub X} and CO emissions. In conjunction with this project, advanced monitoring technologies, such as Ion Sense, and improved sensors for emissions control, such as the AFM1000+ have been developed and commercialized.
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.
Bilocal field theory in four dimensions
Hori, T. )
1993-07-15
A bilocal field theory having Moebius gauge invariance is proposed. In four dimensions there exists a zero momentum state of the first-quantized model which belongs to a nontrivial BRS cohomology class. A field theory Lagrangian having gauge invariance only in four dimensions is constructed.
Continuous point symmetries in group field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2017-03-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on group field theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them.
Quantum equivalence of dual field theories
NASA Astrophysics Data System (ADS)
Fradkin, E. S.; Tseytlin, A. A.
1985-06-01
Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrödinger theory.
Pilot-wave theory and quantum fields
NASA Astrophysics Data System (ADS)
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Quantum Algorithms for Fermionic Quantum Field Theories
2014-04-28
a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by...in fermionic field theories, exemplified by the massive Gross- Neveu model, a theory in two spacetime dimensions with quartic interactions. The...two spacetime dimensions with quartic interactions. Although our analysis is specific to this theory, our algorithm can be adapted to other massive
Field Equations for Space-Time Theory
NASA Astrophysics Data System (ADS)
Bejancu, Aurel
2013-05-01
In the present paper we obtain, in a covariant form, and in their full generality, the field equations in a relativistic general Kaluza-Klein space. This is done by using the Riemannian horizontal connection defined in [3], and some 4D horizontal tensor fields, as for instance: horizontal Ricci tensor, horizontal Einstein gravitational tensor field, horizontal electromagnetic energy-momentum tensor field, etc. Also, we present some inter-relations between STM theory and brane-world theory. This enables us to introduce in brane theory some electromagnetic potentials constructed by means of the warp function.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. 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. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
Yang, Guang; Ren, Zhen; Mei, Yan-Ai
2015-01-01
Previous work from both our lab and others have indicated that exposure to 50 Hz magnetic fields (ELF-MF) was able to modify ion channel functions. However, very few studies have investigated the effects of MF on γ-aminobutyric acid (GABA) type A receptors (GABAARs) channel functioning, which are fundamental to overall neuronal excitability. Here, our major goal is to reveal the potential effects of ELF-MF on GABAARs activity in rat cerebellar granule neurons (CGNs). Our results indicated that exposing CGNs to 1 mT ELF-MF for 60 min. significantly increased GABAAR currents without modifying sensitivity to GABA. However, activation of PKA by db-cAMP failed to do so, but led to a slight decrease instead. On the other hand, PKC activation or inhibition by PMA or Bis and Docosahexaenoic acid (DHA) mimicked or eliminated the field-induced-increase of GABAAR currents. Western blot analysis indicated that the intracellular levels of phosphorylated PKC (pPKC) were significantly elevated after 60 min. of ELF-MF exposure, which was subsequently blocked by application of DHA or EP1 receptor-specific (prostaglandin E receptor 1) antagonist (SC19220), but not by EP2-EP4 receptor-specific antagonists. SC19220 also significantly inhibited the ELF-MF-induced elevation on GABAAR currents. Together, these data obviously demonstrated for the first time that neuronal GABAA currents are significantly increased by ELF-MF exposure, and also suggest that these effects are mediated via an EP1 receptor-mediated PKC pathway. Future work will focus on a more comprehensive analysis of the physiological and/or pathological consequences of these effects. PMID:26176998
Ostrogradsky in theories with multiple fields
Rham, Claudia de; Matas, Andrew
2016-06-23
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
A New Theory of the Electromagnetic Field
NASA Astrophysics Data System (ADS)
Kriske, Richard
2017-01-01
This author has previously introduced a new theory of the Electromagnetic Field and its interaction with matter. There was from the start a problem with Einstein's formulation of Invariants and its use in describing The EM field. The photon produced by first varying a stationary Electric field in one observer's reference frame is not the same as a photon produced from varying the a stationary Magnetic Field. The Magnetic field photon is thought of as being ``off the mass shell''. The Quantum information seems to carry with it an ordering of these events. You see this ordering in Wick's theory and in Feynman diagrams. This author is proposing that other fields can vary first in another Observers reference frame, not just the ``Scalar Field'' or the ``Fermion Field'', but many other forms of Energy. If the ``Nuclear Field'' varies first, it results in Quantum information that produces a photon that has the Nuclear Field in it and also the Magnetic Field, this is the strange effect seen in Nuclear Magnetic Resonance. This author proposed that there is a large number of photons with different properties, because of this ordering of events that occurs in Quantum Information. One of these photons is the Neutrino which appears to be a three field photon. This is Kriske's Field Theory.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
From exceptional field theory to heterotic double field theory via K3
NASA Astrophysics Data System (ADS)
Malek, Emanuel
2017-03-01
In this paper we show how to obtain heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the SL(5) exceptional field theory and show that when the extended space contains a generalised SU(2)-structure manifold one can define a reduction to obtain the heterotic SO(3 , n) double field theory. In this picture, the reduction on the SU(2)-structure breaks half of the supersymmetry of the exceptional field theory and the gauge group of the heterotic double field theory is given by the embedding tensor of the reduction used. Finally, we study the example of a consistent truncation of M-theory on K3 and recover the duality with the heterotic string on T 3. This suggests that the extended space can be made sense of even in the case of non-toroidal compactifications.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D.; Jaervinen, Matti
2009-03-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.
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.
{N}=3 four dimensional field theories
NASA Astrophysics Data System (ADS)
García-Etxebarria, Iñaki; Regalado, Diego
2016-03-01
We introduce a class of four dimensional field theories constructed by quotienting ordinary {N}=4 U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS 5 × (S 5/ ℤ k ). Upon reduction on a circle the {N}=3 theories flow to well-known {N}=6 ABJM theories.
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.
Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
DeTar, Carleton; Winterowd, Christopher; Zafeiropoulos, Savvas
2016-12-01
We report on the first calculation of magnetic catalysis at zero temperature in a fully nonperturbative simulation of the graphene effective field theory. Using lattice gauge theory, a nonperturbative analysis of the theory of strongly interacting, massless, (2 +1 )-dimensional Dirac fermions in the presence of an external magnetic field is performed. We show that in the zero-temperature limit, a nonzero value for the chiral condensate is obtained which signals the spontaneous breaking of chiral symmetry. This result implies a nonzero value for the dynamical mass of the Dirac quasiparticle.
"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.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Conformal field theory on affine Lie groups
Clubok, Kenneth Sherman
1996-04-01
Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.
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.
Weak gravity conjecture and effective field theory
NASA Astrophysics Data System (ADS)
Saraswat, Prashant
2017-01-01
The weak gravity conjecture (WGC) is a proposed constraint on theories with gauge fields and gravity, requiring the existence of light charged particles and/or imposing an upper bound on the field theory cutoff Λ . If taken as a consistency requirement for effective field theories (EFTs), it rules out possibilities for model building including some models of inflation. I demonstrate simple models which satisfy all forms of the WGC, but which through Higgsing of the original gauge fields produce low-energy EFTs with gauge forces that badly violate the WGC. These models illustrate specific loopholes in arguments that motivate the WGC from a bottom-up perspective; for example the arguments based on magnetic monopoles are evaded when the magnetic confinement that occurs in a Higgs phase is accounted for. This indicates that the WGC should not be taken as a veto on EFTs, even if it turns out to be a robust property of UV quantum gravity theories. However, if the latter is true, then parametric violation of the WGC at low energy comes at the cost of nonminimal field content in the UV. I propose that only a very weak constraint is applicable to EFTs, Λ ≲(log 1/g )-1 /2Mpl , where g is the gauge coupling, motivated by entropy bounds. Remarkably, EFTs produced by Higgsing a theory that satisfies the WGC can saturate but not violate this bound.
On space of integrable quantum field theories
NASA Astrophysics Data System (ADS)
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Field theories without a holographic dual
NASA Astrophysics Data System (ADS)
McInnes, Brett
2016-12-01
In applying the gauge-gravity duality to the quark-gluon plasma, one models the plasma using a particular kind of field theory with specified values of the temperature, magnetic field, and so forth. One then assumes that the bulk, an asymptotically AdS black hole spacetime with properties chosen to match those of the boundary field theory, can be embedded in string theory. But this is not always the case: there are field theories with no bulk dual. The question is whether these theories might include those used to study the actual plasmas produced at such facilities as the RHIC experiment or the relevant experiments at the LHC. We argue that, provided that due care is taken to include the effects of the angular momentum associated with the magnetic fields experienced by the plasmas produced by peripheral collisions, the existence of the dual can be established for the RHIC plasmas. In the case of the LHC plasmas, the situation is much more doubtful.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory.
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010); J. Stat. Phys. 149, 643 (2012); J. Stat. Phys. 152, 159 (2013); Phys. Rev. E 83, 041125 (2011)] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Interacting scale invariant but nonconformal field theories
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2017-03-01
There is a dilemma in constructing interacting scale invariant Euclidean field theories that are not conformal invariant. On one hand, scale invariance without conformal invariance seems more generic by requiring only a smaller symmetry. On the other hand, the existence of a nonconserved current with exact scaling dimension d -1 in d dimensions seems to require extra fine-tuning. To understand the competition better, we explore some examples without the reflection positivity. We show that a theory of elasticity (also known as Riva-Cardy theory) coupled with massless fermions in d =4 -ɛ dimensions does not possess an interacting scale invariant fixed point except for an unstable (and unphysical) one with an infinite coefficient of compression. We do, however, find interacting scale invariant but nonconformal field theories in gauge fixed versions of the Banks-Zaks fixed points in d =4 dimensions.
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.
Quantum field theory of treasury bonds.
Baaquie, B E
2001-07-01
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Magnetic monopoles in field theory and cosmology.
Rajantie, Arttu
2012-12-28
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems.
Charge transfer in algebraic quantum field theory
NASA Astrophysics Data System (ADS)
Wright, Jill Dianne
We discuss aspects of the algebraic structure of quantum field theory. We take the view that the superselection structure of a theory should be determinable from the vacuum representation of the observable algebra, and physical properties of the charge. Hence one determines the nature of the charge transfer operations: the automorphisms of the observable algebra corresponding to the movement of charge along space-time paths. New superselection sectors are obtained from the vacuum sector by an automorphism which is a limit of charge transfer operations along paths with an endpoint tending to spacelike infinity. Roberts has shown that for a gauge theory of the first kind, the charge transfer operations for a given charge form a certain kind of 1-cocycle over Minkowski space. The local 1-cohomology group of their equivalence classes corresponds to the superselection structure. The exact definition of the cohomology group depends on the properties of the charge. Using displaced Fock representations of free fields, we develop model field theories which illustrate this structure. The cohomological classification of displaced Fock representations has been elucidated by Araki. For more general representations, explicit determination of the cohomology group is a hard problem. Using our models, we can illustrate ways in which fields with reasonable physical properties depart fromthe abovementioned structure. In 1+1 dimensions, we use the Streater-Wilde model to illustrate explicitly the representation-dependence of the cohomology structure, and the direction-dependence of the limiting charge transfer operation. The cohomology structure may also be representation-dependent in higher-dimensional theories without strict localization of charge, for example the electromagnetic field. The algebraic structure of the electromagnetic field has many other special features, which we discuss in relation to the concept of charge transfer. We also give some indication of the modifications
Diagrammar in classical scalar field theory
Cattaruzza, E.; Gozzi, E.; Francisco Neto, A.
2011-09-15
In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Arrival time in quantum field theory
NASA Astrophysics Data System (ADS)
Wang, Zhi-Yong; Xiong, Cai-Dong; He, Bing
2008-09-01
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.
Recent progress in irrational conformal field theory
Halpern, M.B.
1993-09-01
In this talk, I will review the foundations of irrational conformal field theory (ICFT), which includes rational conformal field theory as a small subspace. Highlights of the review include the Virasoro master equation, the Ward identities for the correlators of ICFT and solutions of the Ward identities. In particular, I will discuss the solutions for the correlators of the g/h coset construction and the correlators of the affine-Sugawara nests on g {contains} h{sub 1} {contains} {hor_ellipsis} {contains} h{sub n}. Finally, I will discuss the recent global solution for the correlators of all the ICFT`s in the master equation.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
A geometric formulation of exceptional field theory
NASA Astrophysics Data System (ADS)
du Bosque, Pascal; Hassler, Falk; Lüst, Dieter; Malek, Emanuel
2017-03-01
We formulate the full bosonic SL(5) exceptional field theory in a coordinateinvariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with SL(5) × ℝ +-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the SL(5) × ℝ +-structure is not locally flat.
Dual field theory of strong interactions
Akers, D.
1987-07-01
A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Near-field optical thin microcavity theory
NASA Astrophysics Data System (ADS)
Wu, Jiu Hui; Hou, Jiejie
2016-01-01
The thin microcavity theory for near-field optics is proposed in this study. By applying the power flow theorem and the variable theorem,the bi-harmonic differential governing equation for electromagnetic field of a three-dimensional thin microcavity is derived for the first time. Then by using the Hankel transform, this governing equation is solved exactly and all the electromagnetic components inside and outside the microcavity can be obtained accurately. According to the above theory, the near-field optical diffraction from a subwavelength aperture embedded in a thin conducting film is investigated, and numerical computations are performed to illustrate the edge effect by an enhancement factor of 1.8 and the depolarization phenomenon of the near-field transmission in terms of the distance from the film surface. This thin microcavity theory is verified by the good agreement between our results and those in the previous literatures. The thin microcavity theory presented in the study should be useful in the possible applications of the thin microcavities in near-field optics and thin-film optics.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Kirby S. Chapman
2004-01-01
During the fourth reporting period, the project team investigated the Non-Selective Catalytic Reduction technologies that are in use on rich-burn four-stroke cycle engines. Several engines were instrumented and data collected to obtain a rich set of engine emissions and performance data. During the data collection, the performance of the catalyst under a variety of operating conditions was measured. This information will be necessary to specify a set of sensors that can then be used to reliably implement NSCRs as plausible technologies to reduce NOx emissions for four-stroke cycle engines used in the E&P industry. A complete summary all the technologies investigated to data is included in the report. For each technology, the summary includes a description of the process, the emission reduction that is to be expected, information on the cost of the technology, development status, practical considerations, compatibility with other air pollutant control technologies, and any references used to obtain the information.
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
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.
Euclidean quantum field theory: Curved spacetimes and gauge fields
NASA Astrophysics Data System (ADS)
Ritter, William Gordon
This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on four-dimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories on curved spacetimes. The success of Euclidean path integrals to capture nonperturbative aspects of QFT has been striking. The Euclidean path integral is the most accurate method of calculating strong-coupling effects in gauge theory (such as glueball masses). Euclidean methods are also useful in the study of black holes, as evidenced by the Hartle-Hawking calculation of black-hole radiance. From a mathematical point of view, on flat spacetimes the Euclidean functional integral provides the most elegant method of constructing examples of interacting relativistic field theories. Yet until now, the incredibly-useful Euclidean path integral had never been given a definitive mathematical treatment on curved backgrounds. It is our aim to rectify this situation. Along the way, we discover that the Dirac operator on an arbitrary Clifford bundle has a resolvent kernel which is the Laplace transform of a positive measure. In studying spacetime symmetries, we discover a new way of constructing unitary representations of noncompact Lie groups. We also define and explore an interesting notion of convergence for Laplacians. The same mathematical framework applies to scalar fields, fermions, and gauge fields. The later chapters are devoted to gauge theory. We present a rigorous, self-contained introduction to the subject, aimed at mathematicians and using the language of modern mathematics, with a view towards nonperturbative renormalization in four dimensions. The latter ideas are unfinished. A completion of the final chapter would imply the construction
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with the remarkable observation of Cardy that the horizontal crossing probability of critical percolation may be computed analytically within the formalism of boundary conformal field theory. Cardy’s derivation relies on certain implicit assumptions which are shown to lead inexorably to indecomposable modules and logarithmic singularities in correlators. For this, a short introduction to the fusion algorithm of Nahm, Gaberdiel and Kausch is provided. While the percolation logarithmic conformal field theory is still not completely understood, there are several examples for which the formalism familiar from rational conformal field theory, including bulk partition functions, correlation functions, modular transformations, fusion rules and the Verlinde formula, has been successfully generalized. This is illustrated for three examples: the singlet model \\mathfrak {M} (1,2), related to the triplet model \\mathfrak {W} (1,2), symplectic fermions and the fermionic bc ghost system; the fractional level Wess-Zumino-Witten model based on \\widehat{\\mathfrak {sl}} \\left( 2 \\right) at k=-\\frac{1}{2}, related to the bosonic βγ ghost system; and the Wess-Zumino-Witten model for the Lie supergroup \\mathsf {GL} \\left( 1 {\\mid} 1 \\right), related to \\mathsf {SL} \\left( 2 {\\mid} 1 \\right) at k=-\\frac{1}{2} and 1, the Bershadsky-Polyakov algebra W_3^{(2)} and the Feigin-Semikhatov algebras W_n^{(2)}. These examples have been chosen because they represent the most accessible, and most useful, members of the three best-understood families of logarithmic conformal field theories. The logarithmic minimal models \\mathfrak {W} (q,p), the fractional level Wess-Zumino-Witten models, and the Wess-Zumino-Witten models on Lie supergroups (excluding \\mathsf {OSP} \\left( 1 {\\mid} 2n \\right)). In this review, the emphasis lies on the representation theory
Causality constraints in conformal field theory
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-17
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (Φ)^{4} coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators
Causality constraints in conformal field theory
NASA Astrophysics Data System (ADS)
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Mean-field kinetic nucleation theory
NASA Astrophysics Data System (ADS)
Kalikmanov, V. I.
2006-03-01
A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
An Introduction to Effective Field Theory
NASA Astrophysics Data System (ADS)
Burgess, C. P.
2007-11-01
This review summarizes effective field theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described and evaluated explicitly for a simple model. Power-counting results are illustrated for a few cases of practical interest, and several applications to quantum electrodynamics are described.
Effective Field Theories of Nuclear Structure
NASA Astrophysics Data System (ADS)
Furnstahl, Richard
1996-10-01
Traditional nuclear structure calculations have been pushed to new heights recently by exploiting new methods and increased computational power.(B. Pudliner et al)., Phys. Rev. Lett. 74, 4396 (1995); S.E. Koonin et al., nucl-th/9602006 (1996). Nevertheless, these developments have been made without direct input from quantum chromodynamics (QCD), the basic theory of strong interactions. Effective Field Theory provides a framework for connecting the energy scales and degrees of freedom appropriate for nuclear structure with those in the underlying QCD. Recent work shows how spontaneously broken chiral symmetry constrains the systematics of few-body nuclei.(See, for example, J.L. Friar, Few-Body Systems Suppl. 99), 1 (1996). Important ingredients are dimensional power counting and the assumption of naturalness,(A. Manohar and H. Georgi, Nucl. Phys. B234), 189 (1984). which allow estimates of the sizes of terms in effective lagrangians and imply the hierarchy of nuclear many-body forces. The delicacies of nuclear saturation introduce formidable obstacles to the systematic extension of effective chiral field theory to finite densities. For heavier nuclei, however, the successes of relativistic mean-field phenomenology can be understood in terms of nonrenormalizable effective field theories that are consistent with the symmetries of QCD. This framework provides new insight into issues of relativistic versus nonrelativistic formulations, nucleon compositeness, vacuum contributions, and extrapolations to high density.
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.
Dirac-Kaehler Theory and Massless Fields
Pletyukhov, V. A.; Strazhev, V. I.
2010-03-24
Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
A periodic table of effective field theories
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2017-02-01
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.
A computational theory of visual receptive fields.
Lindeberg, Tony
2013-12-01
A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative
Extending Gurwitsch's field theory of consciousness.
Yoshimi, Jeff; Vinson, David W
2015-07-01
Aron Gurwitsch's theory of the structure and dynamics of consciousness has much to offer contemporary theorizing about consciousness and its basis in the embodied brain. On Gurwitsch's account, as we develop it, the field of consciousness has a variable sized focus or "theme" of attention surrounded by a structured periphery of inattentional contents. As the field evolves, its contents change their status, sometimes smoothly, sometimes abruptly. Inner thoughts, a sense of one's body, and the physical environment are dominant field contents. These ideas can be linked with (and help unify) contemporary theories about the neural correlates of consciousness, inattention, the small world structure of the brain, meta-stable dynamics, embodied cognition, and predictive coding in the brain.
Gauge Field Theories, 2nd Edition
NASA Astrophysics Data System (ADS)
Frampton, Paul H.
2000-08-01
The first edition of Gauge Field Theories, published in 1985, quickly became widely used in universities and other institutions of higher learning around the world. Written by well-known physicist Paul Frampton, the new edition continues to offer a first-rate mathematical treatment of gauge field theories, while thoroughly updating all chapters to keep pace with developments in the field. Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research. Special features of the Second Edition include: * Improved, logical organization of the material on gauge invariance, quantization, and renormalization * Major revision of the chapter on electroweak interactions, incorporating the latest precision data and discovery of the top quark * Discussions of renormalization group and quantum chromodynamics * A completely new chapter on model building
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Recursion equations in gauge field theories
NASA Astrophysics Data System (ADS)
Migdal, A. A.
An approximate recursion equation is formulated, describing the scale transformation of the effective action of a gauge field. In two-dimensional space-time the equation becomes exact. In four-dimensional theories it reproduces asymptotic freedom to an accuracy of 30% in the coefficients of the β-function. In the strong-coupling region the β-function remains negative and this results in an asymptotic prison in the infrared region. Possible generalizations and applications to the quark-gluon gauge theory are discussed.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Free □ k scalar conformal field theory
NASA Astrophysics Data System (ADS)
Brust, Christopher; Hinterbichler, Kurt
2017-02-01
We consider the generalizations of the free U( N ) and O( N ) scalar conformal field theories to actions with higher powers of the Laplacian □ k , in general dimension d. We study the spectra, Verma modules, anomalies and OPE of these theories. We argue that in certain d and k, the spectrum contains zero norm operators which are both primary and descendant, as well as extension operators which are neither primary nor descendant. In addition, we argue that in even dimensions d ≤ 2 k, there are well-defined operator algebras which are related to the □ k theories and are novel in that they have a finite number of single-trace states.
Operator algebra in logarithmic conformal field theory
Nagi, Jasbir
2005-10-15
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the extensions of this machinery to the logarithmic case are studied and used. More precisely, from Moebius symmetry constraints, the generic three- and four-point functions of logarithmic quasiprimary fields are calculated in closed form for arbitrary Jordan rank. As an example, c=0 disordered systems with nondegenerate vacua are studied. With the aid of two-, three-, and four-point functions, the operator algebra is obtained and associativity of the algebra studied.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Effective Field Theory for Rydberg Polaritons
NASA Astrophysics Data System (ADS)
Gullans, M. J.; Thompson, J. D.; Wang, Y.; Liang, Q.-Y.; Vuletić, V.; Lukin, M. D.; Gorshkov, A. V.
2016-09-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one-dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a nonequilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N -body interactions between Rydberg polaritons. These results pave the way towards studying nonperturbative effects in quantum field theories using Rydberg polaritons.
Effective Field Theory for Rydberg Polaritons
Gullans, M. J.; Thompson, J. D.; Wang, Y.; Liang, Q.-Y.; Vuletić, V.; Lukin, M. D.; Gorshkov, A. V.
2016-01-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a non-equilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying non-perturbative effects in quantum field theories using Rydberg polaritons. PMID:27661685
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Superconformal field theories from M-theory crystal lattices
NASA Astrophysics Data System (ADS)
Lee, Sangmin
2007-05-01
We propose a brane configuration for the (2+1)d, N=2 superconformal theories (CFT3) arising from M2 branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT4. The fundamental fields of the CFT3 are M2-brane discs localized around the intersections, and the superpotential terms are identified with the atoms of the crystal. The model correctly reproduces the Bogomol’nyi-Prasad-Sommerfield (BPS) spectrum of mesons.
Higher spin double field theory: a proposal
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Park, Jeong-Hyuck
2016-07-01
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Generalized IIB supergravity from exceptional field theory
NASA Astrophysics Data System (ADS)
Baguet, Arnaud; Magro, Marc; Samtleben, Henning
2017-03-01
The background underlying the η-deformed AdS 5 × S 5 sigma-model is known to satisfy a generalization of the IIB supergravity equations. Their solutions are related by T-duality to solutions of type IIA supergravity with non-isometric linear dilaton. We show how the generalized IIB supergravity equations can be naturally obtained from exceptional field theory. Within this manifestly duality covariant formulation of maximal supergravity, the generalized IIB supergravity equations emerge upon imposing on the fields a simple Scherk-Schwarz ansatz which respects the section constraint.
The Supersymmetric Effective Field Theory of Inflation
NASA Astrophysics Data System (ADS)
Delacrétaz, Luca V.; Gorbenko, Victor; Senatore, Leonardo
2017-03-01
We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable Stückelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplifying the analysis in this regime. We study the phenomenology of this Lagrangian. The Goldstino can have a non-relativistic dispersion relation. Gravitino and Goldstino affect the primordial curvature perturbations at loop level. The UV modes running in the loops generate three-point functions which are degenerate with the ones coming from operators already present in the absence of supersymmetry. Their size is potentially as large as corresponding to f NL equil., orthog. ˜ 1 or, for particular operators, even ≫ 1. The non-degenerate contribution from modes of order H is estimated to be very small.
Backreacted axion field ranges in string theory
NASA Astrophysics Data System (ADS)
Baume, Florent; Palti, Eran
2016-08-01
String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter controlling the effective decay constant is unconstrained by tadpoles and can in principle lead to an arbitrarily large effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement leaving a sub-Planckian effective decay constant.
Effective Particles in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Głazek, Stanisław D.; Trawiński, Arkadiusz P.
2017-03-01
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead integrates out the large changes of invariant mass. The new procedure is explained using examples of known interactions. Some applications in phenomenology, including processes measurable in colliders, are briefly presented.
Hamiltonian formulation of string field theory
NASA Astrophysics Data System (ADS)
Siopsis, George
1987-09-01
Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.
Superconformal partial waves in Grassmannian field theories
NASA Astrophysics Data System (ADS)
Doobary, Reza; Heslop, Paul
2015-12-01
We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr( m| n, 2 m|2 n) for all m, n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM ( m = n = 2) and in N = 2 superconformal field theories in four dimensions ( m = 2 , n = 1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories ( m = 2 , n = 0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2 n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU( N) gauge theory at finite N. The <2233> correlator predicts a non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is precisely one such protected twist four operator for each spin.
Fermionic ghosts in Moyal string field theory
NASA Astrophysics Data System (ADS)
Bars, Itzhak; Kishimoto, Isao; Matsuo, Yutaka
2003-07-01
We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been used in our previous publications. This paper provides the technical details of the computations which were omitted there.
Nonperturbative studies in quantum field theory
Abada, A.
1992-01-01
This dissertation is composed of three different research topics. The first part deals with the Study of the so-called local lattice Yukawa theory. The motivation for this study is to investigate the interior of the phase diagram of this theory. A strong y expansion (y being the bare Yukawa coupling) is performed of the partition function and show that within the (finite) range of convergence of the series expansion, the lattice Yukawa theory is equivalent to a purely bosonic theory, with a shifted action. The author explicitly calculated the shifted action to the fourth order in 1/y and find that it is composed of competing interactions. This suggests that away from y = [infinity] towards the interior of the phase diagram, there is a more complicated ordering than simple ferromagnetic or antiferromagnetic. In the second part, the question is addressed of formation of bound states out of constituent fields in an exactly soluble theory, i.e. multifermion electro-dynamics in two space-time dimensions. The author exactly calculates the correlation function corresponding to a neutral composite fermion operator and discuss the pole structure of its Fourier transform. It does not exhibit a simple pole in p[sup 2], hence the corresponding neutral composite operator does not create an asymptotic state in the spectrum of the theory. In part three, the author puts multifermion QED[sub 2] in a heat bath and address the same question as in part two. The author first exactly calculates a bosonic correlation function at finite temperature and density, and discuss its behavior. The author then exactly calculates the correlation function corresponding to the neutral composite fermion operator at finite temperature and density and discusses its behavior. It is concluded that the temperature does not help the composite fermion operator create a particle in the spectrum of the theory.
Emergent coherent structures in nonequilibrium field theory
NASA Astrophysics Data System (ADS)
Thorarinson, Joel Larus Marvin
2008-10-01
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field theories with symmetry breaking scenarios and since they drastically change the power spectrum, understanding their properties and lifetimes is essential for characterization of the equilibration time scales of a given system. To understand the mechanisms of their creation we rely on large scale computations to solve the fully nonlinear equations of motion. By using both Langevin thermalization techniques and various ansatz we find information about both the individual formation and stability properties of these structures and their effect on global observables such as the decay rate of a metastable vacuum. Each of these aspects contains surprises and radical departures from the linearized theories. We also show examples of how these structures can be examined in momentum space from computing several correlation functions. We extend 2d results on the effect of these emergent structures to the decay rate of a false vacuum to 3d and confirm that these time-dependent structures modify the decay, after a quench, to a power law in pure scalar theories. Adding gauge fields, we present new time dependent nontopological solutions in the 2d Abelian Higgs model which show the creation of oscillons from vortex antivortex annihilations. A phase transition in configuration space is then constructed from the stability properties of these oscillons in parameter space. Similarly, in 3 d we show that oscillons may be formed through toroidal ux-tube annihilations. Finally, these properties are shown to also apply to more complex situations, such as the condensed proton-neutron system, which exhibits all the previous oscillon results as well as a new nontrivial vortex-vortex bound state.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Causality constraints in conformal field theory
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-17
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well knownmore » sign constraint on the (Φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators« less
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Bayesian parameter estimation for effective field theories
NASA Astrophysics Data System (ADS)
Wesolowski, S.; Klco, N.; Furnstahl, R. J.; Phillips, D. R.; Thapaliya, A.
2016-07-01
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
The effective field theory of dark energy
Gubitosi, Giulia; Vernizzi, Filippo; Piazza, Federico E-mail: fpiazza@apc.univ-paris7.fr
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Feynman-Schwinger technique in field theories
NASA Astrophysics Data System (ADS)
Şavkli, Çetin
2001-02-01
In these lectures we introduce the Feynman-Schwinger representation method for solying nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving nonperturbative problems. Then we discuss the Feynman-Schwinger (FSR) representation method with applications to scalar interactions. The FSR approach is a continuum path integral integral approach in terms of covariant trajectories of particles. Using the exact results provided by the FSR approach we test the reliability of commonly used approximations for nonperturbative summation of interactions for few body systems.
A matrix model from string field theory
NASA Astrophysics Data System (ADS)
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
Exact integrability in quantum field theory
Thacker, H.B.
1980-08-01
The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)
The Effective Field Theory of nonsingular cosmology
NASA Astrophysics Data System (ADS)
Cai, Yong; Wan, Youping; Li, Hai-Guang; Qiu, Taotao; Piao, Yun-Song
2017-01-01
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory (EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological model, and show the perturbation spectrum can be consistent with the observations.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
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.
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.
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.
Thermal field theories and shifted boundary conditions
NASA Astrophysics Data System (ADS)
Giusti, L.; Meyer, H.
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.
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.
Refringence, field theory and normal modes
NASA Astrophysics Data System (ADS)
Barceló, Carlos; Liberati, Stefano; Visser, Matt
2002-06-01
In a previous paper [Barceló C et al 2001 Class. Quantum Grav. 18 3595-610 (Preprint gr-qc/0104001)] we have shown that the occurrence of curved spacetime 'effective Lorentzian geometries' is a generic result of linearizing an arbitrary classical field theory around some nontrivial background configuration. This observation explains the ubiquitous nature of the 'analogue models' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analysed in our previous paper, there is a single unique effective metric; more complicated situations can lead to bi-metric and multi-metric theories. In the present paper we will investigate the conditions required to keep the situation under control and compatible with experiment - either by enforcing a unique effective metric (as would be required to be strictly compatible with the Einstein equivalence principle), or at the worst by arranging things so that there are multiple metrics that are all 'close' to each other (in order to be compatible with the Eötvös experiment). The algebraically most general situation leads to a physical model whose mathematical description requires an extension of the usual notion of Finsler geometry to a Lorentzian-signature pseudo-Finsler geometry; while this is possibly of some interest in its own right, this particular case does not seem to be immediately relevant for either particle physics or gravitation. The key result is that wide classes of theories lend themselves to an effective metric description. This observation provides further evidence that the notion of 'analogue gravity' is rather generic.
Homogeneous cosmologies as group field theory condensates
NASA Astrophysics Data System (ADS)
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2014-06-01
We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the `condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.
Quantum Field Theory in Condensed Matter Physics
NASA Astrophysics Data System (ADS)
Tsvelik, Alexei M.
2007-01-01
Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34
Greg Beshouri; Kirby S. Chapman; Jim McCarthy; Sarah R. Nuss-Warren; Mike Whelan
2006-03-01
This quarterly report re-evaluates current market objectives in the exploration and production industry, discusses continuing progress in testing that evaluates emission control technologies applied to a two-stroke cycle natural gas-fueled engine, and presents a scheme for enacting remote monitoring and control of engines during upcoming field tests. The examination of current market objectives takes into account technological developments and changing expectations for environmental permitting which may have occurred over the last year. This demonstrates that the continuing work in controlled testing and toward field testing is on track Market pressures currently affecting the gas exploration and production industry are shown to include a push for increased production, as well as an increasing cost for environmental compliance. This cost includes the direct cost of adding control technologies to field engines as well as the indirect cost of difficulty obtaining permits. Environmental regulations continue to require lower emissions targets, and some groups of engines which had not previously been regulated will be required to obtain permits in the future. While the focus remains on NOx and CO, some permits require reporting of additional emissions chemicals. Continuing work in controlled testing uses a one cylinder Ajax DP-115 (a 13.25 in bore x 16 in stroke, 360 rpm engine) to assess a sequential analysis and evaluation of a series of engine upgrades. As with most of the engines used in the natural gas industry, the Ajax engine is a mature engine with widespread usage throughout the gas gathering industry. The end point is an assessment of these technologies that assigns a cost per unit reduction in NOx emissions. Technologies including one pre-combustion chamber, in-cylinder sensors, the means to adjust the air-to-fuel ratio, and modification of the air filter housing have been evaluated in previous reports. Current work focuses on final preparations for testing
Kirby S. Chapman; Sarah R. Nuss-Warren
2006-07-01
Continuing work in controlled testing uses a one cylinder Ajax DP-115 (a 13.25 in bore x 16 in stroke, 360 rpm engine) to assess a sequential analysis and evaluation of a series of engine upgrades. As with most of the engines used in the natural gas industry, the Ajax engine is a mature engine with widespread usage throughout the gas gathering industry. The end point is an assessment of these technologies that assigns a cost per unit reduction in NOX emissions. Technologies including one pre-combustion chamber, in-cylinder sensors, the means to adjust the air-to-fuel ratio, and modification of the air filter housing have been evaluated in previous reports. Current work focuses on final preparations for testing pre-combustion chambers with different characteristics and using mid-to-high-pressure fuel valves and initial runs of these tests. By using the Ajax DP-115 these tests are completed in a low-cost and efficient manner. The various technologies can be quickly exchanged with different hardware, and it is inexpensive to run the engine. Progress in moving toward field testing is discussed, and changes to the first planned field test are presented. Although changes have been made to the previous plan, it is expected that several new sites will be selected soon. Field tests will begin in the next quarter.
Characterization of Pressure Transients Generated by Nanosecond Electrical Pulse (nsEP) Exposure.
Roth, Caleb C; Barnes, Ronald A; Ibey, Bennett L; Beier, Hope T; Christopher Mimun, L; Maswadi, Saher M; Shadaram, Mehdi; Glickman, Randolph D
2015-10-09
The mechanism(s) responsible for the breakdown (nanoporation) of cell plasma membranes after nanosecond pulse (nsEP) exposure remains poorly understood. Current theories focus exclusively on the electrical field, citing electrostriction, water dipole alignment and/or electrodeformation as the primary mechanisms for pore formation. However, the delivery of a high-voltage nsEP to cells by tungsten electrodes creates a multitude of biophysical phenomena, including electrohydraulic cavitation, electrochemical interactions, thermoelastic expansion, and others. To date, very limited research has investigated non-electric phenomena occurring during nsEP exposures and their potential effect on cell nanoporation. Of primary interest is the production of acoustic shock waves during nsEP exposure, as it is known that acoustic shock waves can cause membrane poration (sonoporation). Based on these observations, our group characterized the acoustic pressure transients generated by nsEP and determined if such transients played any role in nanoporation. In this paper, we show that nsEP exposures, equivalent to those used in cellular studies, are capable of generating high-frequency (2.5 MHz), high-intensity (>13 kPa) pressure transients. Using confocal microscopy to measure cell uptake of YO-PRO®-1 (indicator of nanoporation of the plasma membrane) and changing the electrode geometry, we determined that acoustic waves alone are not responsible for poration of the membrane.
Characterization of Pressure Transients Generated by Nanosecond Electrical Pulse (nsEP) Exposure
NASA Astrophysics Data System (ADS)
Roth, Caleb C.; Barnes, Ronald A., Jr.; Ibey, Bennett L.; Beier, Hope T.; Christopher Mimun, L.; Maswadi, Saher M.; Shadaram, Mehdi; Glickman, Randolph D.
2015-10-01
The mechanism(s) responsible for the breakdown (nanoporation) of cell plasma membranes after nanosecond pulse (nsEP) exposure remains poorly understood. Current theories focus exclusively on the electrical field, citing electrostriction, water dipole alignment and/or electrodeformation as the primary mechanisms for pore formation. However, the delivery of a high-voltage nsEP to cells by tungsten electrodes creates a multitude of biophysical phenomena, including electrohydraulic cavitation, electrochemical interactions, thermoelastic expansion, and others. To date, very limited research has investigated non-electric phenomena occurring during nsEP exposures and their potential effect on cell nanoporation. Of primary interest is the production of acoustic shock waves during nsEP exposure, as it is known that acoustic shock waves can cause membrane poration (sonoporation). Based on these observations, our group characterized the acoustic pressure transients generated by nsEP and determined if such transients played any role in nanoporation. In this paper, we show that nsEP exposures, equivalent to those used in cellular studies, are capable of generating high-frequency (2.5 MHz), high-intensity (>13 kPa) pressure transients. Using confocal microscopy to measure cell uptake of YO-PRO®-1 (indicator of nanoporation of the plasma membrane) and changing the electrode geometry, we determined that acoustic waves alone are not responsible for poration of the membrane.
Characterization of Pressure Transients Generated by Nanosecond Electrical Pulse (nsEP) Exposure
Roth, Caleb C.; Barnes Jr., Ronald A.; Ibey, Bennett L.; Beier, Hope T.; Christopher Mimun, L.; Maswadi, Saher M.; Shadaram, Mehdi; Glickman, Randolph D.
2015-01-01
The mechanism(s) responsible for the breakdown (nanoporation) of cell plasma membranes after nanosecond pulse (nsEP) exposure remains poorly understood. Current theories focus exclusively on the electrical field, citing electrostriction, water dipole alignment and/or electrodeformation as the primary mechanisms for pore formation. However, the delivery of a high-voltage nsEP to cells by tungsten electrodes creates a multitude of biophysical phenomena, including electrohydraulic cavitation, electrochemical interactions, thermoelastic expansion, and others. To date, very limited research has investigated non-electric phenomena occurring during nsEP exposures and their potential effect on cell nanoporation. Of primary interest is the production of acoustic shock waves during nsEP exposure, as it is known that acoustic shock waves can cause membrane poration (sonoporation). Based on these observations, our group characterized the acoustic pressure transients generated by nsEP and determined if such transients played any role in nanoporation. In this paper, we show that nsEP exposures, equivalent to those used in cellular studies, are capable of generating high-frequency (2.5 MHz), high-intensity (>13 kPa) pressure transients. Using confocal microscopy to measure cell uptake of YO-PRO®-1 (indicator of nanoporation of the plasma membrane) and changing the electrode geometry, we determined that acoustic waves alone are not responsible for poration of the membrane. PMID:26450165
Geomagnetic Field -- From Paleomagnetism to Dynamo Theory
NASA Astrophysics Data System (ADS)
Kono, M.
2008-05-01
Since 1995, self-consistent models of the geodynamo became available. There are certain problems, but some of these models have shown behaviors quite similar to those observed by paleomagnetism, including polarity reversals (Kono and Roberts, 2002). There is thus a hope that the combination of paleomagnetism and dynamo theory may provide us a very comprehensive understanding of the geomagnetic field. In this paper, I will try to highlight the possibilities and limitations in such studies. From satellite observations, it was shown that the power of the magnetic field contained in each degree is nearly the same if measured at the core-mantle boundary (CMB). The core field can be seen only to degree 13 or 14 where the field power is about (10 nT)2. Beyond that, the crustal magnetization dominates and the core signal is lost. The value of 10 nT is far larger than the accuracy of the present-day instruments, but much smaller than the resolution obtainable by paleomagnetic observations. We may safely assume that the error in paleomagnetic measurements (in direction) is of the order of 10 degrees. This error corresponds to the resolution of about 1/5. The relative powers of the low degree terms in the magnetic field at the surface are 1.0, 0.033, 0.019, 0.0055 (Langel and Estes, 1982). This means that only the degrees 1 to 3 terms may be distinguished by paleomagnetic data. From the combination of dipole, quadrupole, and octupole, what we can deduce about the fundamental properties of the geomagnetic field? Here are some of the possibilities, which may give important clues when we compare with dynamo simulation results. (1) The current dipole power is several times larger than the value expected from the trend line produced by degrees 2--13. Is this a persistent feature or transient? (2) In PSV analysis, the angular standard deviation increases with latitude. Kono and Tanaka (1995) showed that it is possible only if the (2,1) (degree, order) or (3,2) term is very large
Star democracy in open string field theory
NASA Astrophysics Data System (ADS)
Maccaferri, Carlo; Mamone, Davide
2003-09-01
We study three types of star products in SFT: the ghosts, the twisted ghosts and the matter. We find that their Neumann coefficients are related to each other in a compact way which includes the Gross-Jevicki relation between matter and ghost sector: we explicitly show that the same relation, with a minus sign, holds for the twisted and nontwisted ghosts (which are different but define the same solution). In agreement with this, we prove that matter and twisted ghost coefficients just differ by a minus sign. As a consistency check, we also compute the spectrum of the twisted ghost vertices from conformal field theory and, using equality of twisted and reduced slivers, we derive the spectrum of the non twisted ghost star.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
2014-03-01
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Effective field theory for cold atoms
Hammer, H.-W.
2005-05-06
Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms. Recent extensions of this approach to the four-body system and N-boson droplets in two spatial dimensions will also be discussed.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
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.
Neural field theory with variance dynamics.
Robinson, P A
2013-06-01
Previous neural field models have mostly been concerned with prediction of mean neural activity and with second order quantities such as its variance, but without feedback of second order quantities on the dynamics. Here the effects of feedback of the variance on the steady states and adiabatic dynamics of neural systems are calculated using linear neural field theory to estimate the neural voltage variance, then including this quantity in the total variance parameter of the nonlinear firing rate-voltage response function, and thus into determination of the fixed points and the variance itself. The general results further clarify the limits of validity of approaches with and without inclusion of variance dynamics. Specific applications show that stability against a saddle-node bifurcation is reduced in a purely cortical system, but can be either increased or decreased in the corticothalamic case, depending on the initial state. Estimates of critical variance scalings near saddle-node bifurcation are also found, including physiologically based normalizations and new scalings for mean firing rate and the position of the bifurcation.
Propagation in polymer parameterised field theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
2017-01-01
The Hamiltonian constraint operator in loop quantum gravity acts ultralocally. Smolin has argued that this ultralocality seems incompatible with the existence of a quantum dynamics which propagates perturbations between macroscopically seperated regions of quantum geometry. We present evidence to the contrary within an LQG type ‘polymer’ quantization of two dimensional parameterised field theory (PFT). PFT is a generally covariant reformulation of free field propagation on flat spacetime. We show explicitly that while, as in LQG, the Hamiltonian constraint operator in PFT acts ultralocally, states in the joint kernel of the Hamiltonian and diffeomorphism constraints of PFT necessarily describe propagation effects. The particular structure of the finite triangulation Hamiltonian constraint operator plays a crucial role, as does the necessity of imposing (the continuum limit of) its kinematic adjoint as a constraint. Propagation is seen as a property encoded by physical states in the kernel of the constraints rather than that of repeated actions of the finite triangulation Hamiltonian constraint on kinematic states. The analysis yields robust structural lessons for putative constructions of the Hamiltonian constraint in LQG for which ultralocal action co-exists with a description of propagation effects by physical states.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological field theory of dynamical systems.
Ovchinnikov, Igor V
2012-09-01
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological field theory of dynamical systems
NASA Astrophysics Data System (ADS)
Ovchinnikov, Igor V.
2012-09-01
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
Mean Field Theories of Icosahedral Quasicrystals.
NASA Astrophysics Data System (ADS)
Troian, Sandra Marina
studied. We also rederive and generalize a model free energy presented by Kalugin et al. to show that their original conclusion of a metastable quasicrystal is invalidated by the inclusion of a local quartic term in the free energy. Lastly, we review three other mean field theories recently proposed to explain the existence of quasicrystals.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
Halo nuclei interactions using effective field theory
NASA Astrophysics Data System (ADS)
Fernando, Nippalage Lakma Kaushalya
Effective field theory (EFT) provides a framework to exploit separation of scales in the physical system in order to perform systematic model-independent calculations. There has been significant interest in applying the methods of EFT to halo nuclei. Using halo effective field theory, I provide a model-independent calculation of the radiative neutron capture on lithium-7 over an energy range where the contribution from the 3+ resonance becomes important. This reaction initiate the sequence in the carbon-nitrogen-oxygen (CNO) cycle in the inhomogeneous BBN models, and determine the amount of heavy element production from its reaction rate. One finds that a satisfactory description of the capture reaction, in the present single-particle approximation, suggests the use of a resonance width about three times larger than the experimental value. Power counting arguments that establish a hierarchy for the electromagnetic one- and two-body currents is also presented. The neutron capture of Lithium7 calculation has direct impact on the proton capture on beryllium7 which plays an important role in the neutrino experiments studying physics beyond the Standard Model of particle physics. As a further study of halo nuclei interactions, the cross section of radiative capture of a neutron by carbon-14 is calculated by considering the dominant contribution from electric dipole transition. This is also a part of the CNO cycle and as the slowest reaction in the chain it limits the flow of the production of heavier nuclei A > 14. The cross section is expressed in terms of the elastic scattering parameters of an effective range expansion. Contributions from both the resonant and non-resonant interactions are calculated. Significant interferences between these leads to a capture contribution that deviates from a simple Breit-Wigner resonance form. Using EFT, I present electromagnetic form factors of several halo nuclei. The magnetic dipole moment and the charge radii of carbon-15
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
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.
Gravitational radiative corrections from effective field theory
Goldberger, Walter D.; Ross, Andreas
2010-06-15
In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures 'post-Minkowskian' corrections to the multipole expansion due to nonlinear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from nonrelativistic binaries, including long distance effects up to 3 post-Newtonian (v{sup 6}) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.
Protected gates for topological quantum field theories
Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit
2016-02-15
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Quarkonium hybrids with nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Berwein, Matthias; Brambilla, Nora; Tarrús Castellà, Jaume; Vairo, Antonio
2015-12-01
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass m of the heavy quark. At order 1 /m in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as Λ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for c c ¯, b c ¯, and b b ¯ hybrids. The Λ -doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.
Field Theories from the Relativistic Law of Motion
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Dadhich, Naresh
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in four-velocity of the particle. The linear law leads to the vector gauge theory which could be the Abelian Maxwell electrodynamics or the non-Abelian Yang-Mills theory. On the other hand, the quadratic law demands space-time metric as its potential which is equivalent to demanding the principle of equivalence. It leads to the tensor theory of gravitational field - general relativity. It is remarkable that a purely dynamical property of the force law leads uniquely to the corresponding field theories.
A Geometrically Nonlinear Phase Field Theory of Brittle Fracture
2014-10-01
A Geometrically Nonlinear Phase Field Theory of Brittle Fracture by JD Clayton and J Knap ARL-RP-0511 October 2014...21005-5069 ARL-RP-0511 October 2014 A Geometrically Nonlinear Phase Field Theory of Brittle Fracture JD Clayton and J Knap Weapons and...Nonlinear Phase Field Theory of Brittle Fracture 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) JD Clayton
Effective field theories for muonic hydrogen
NASA Astrophysics Data System (ADS)
Peset, Clara
2017-03-01
Experimental measurements of muonic hydrogen bound states have recently started to take place and provide a powerful setting in which to study the properties of QCD. We profit from the power of effective field theories (EFTs) to provide a theoretical framework in which to study muonic hydrogen in a model independent fashion. In particular, we compute expressions for the Lamb shift and the hyperfine splitting. These expressions include the leading logarithmic O(mμα6) terms, as well as the leading {\\cal O}≤ft( {{m_μ }{α ^5}{{m_μ ^2} \\over {Λ {{QCD}}^2}}} \\right) hadronic effects. Most remarkably, our analyses include the determination of the spin-dependent and spin-independent structure functions of the forward virtualphoton Compton tensor of the proton to O(p3) in HBET and including the Delta particle. Using these results we obtain the leading hadronic contributions to the Wilson coeffcients of the lepton-proton four fermion operators in NRQED. The spin-independent coeffcient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, which is the main source of uncertainty in our computation. The spindependent coeffcient yields the prediction of the hyperfine splitting. The use of EFTs crucially helps us organizing the computation, in such a way that we can clearly address the parametric accuracy of our result. Furthermore, we review in the context of NRQED all the contributions to the energy shift of O(mμα5, as well as those that scale like mrα6× logarithms.
Variational principles for multisymplectic second-order classical field theories
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015-06-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
The State of the Field: Interdisciplinary Theory
ERIC Educational Resources Information Center
Newell, William H.
2013-01-01
This chronological overview of the development of interdisciplinary theory starts with the pre-cursors of theory: the development and elaboration of the definition of interdisciplinary studies, influential but problematic images of interdisciplinary studies proposed by Donald Campbell and Erich Jantsch, and best practices in interdisciplinary…
Parastatistics and conformal field theories in two dimensions
NASA Astrophysics Data System (ADS)
Mansouri, Freydoon; Wu, Xizeng
1989-04-01
The relation between parafermion field theories of order Q and the corresponding fermion field theories with SO(Q) symmetry is studied. It is shown that these theories are related but not identical. The explicit relation between the states and the observables of the two classes of theories are given without using the Klein transformations. The formalism is applied to the free conformally invariant parafermion theories in two dimensions. Their Virasoro algebra and SO(N) Kac-Moody algebra are given. The equivalence of their canonical form of the energy-momentum tensor with the Sugawara-Sommerfield form is also elucidated.
Towards a double field theory on para-Hermitian manifolds
NASA Astrophysics Data System (ADS)
Vaisman, Izu
2013-12-01
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.
Towards a double field theory on para-Hermitian manifolds
Vaisman, Izu
2013-12-15
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.
Stability in higher-derivative matter fields theories
NASA Astrophysics Data System (ADS)
Tretyakov, Petr V.
2016-09-01
We discuss possible instabilities in higher-derivative matter field theories. These theories have two free parameters β _1 and β _4. By using a dynamical system approach we explicitly demonstrate that for the stability of Minkowski space in an expanding universe we need the condition β _4<0. By using the quantum field theory approach we also find an additional restriction for the parameters, β _1>-1/3β _4, which is needed to avoid a tachyon-like instability.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Effective field theory of broken spatial diffeomorphisms
Lin, Chunshan; Labun, Lance Z.
2016-03-17
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constantmore » for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. In conclusion, we discuss several examples relevant to theories of massive gravity.« less
Effective field theory of broken spatial diffeomorphisms
Lin, Chunshan; Labun, Lance Z.
2016-03-17
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. In conclusion, we discuss several examples relevant to theories of massive gravity.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
Flat holography: aspects of the dual field theory
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2016-12-01
Assuming the existence of a field theory in D dimensions dual to ( D + 1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D = 4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.
Comparisons and connections between mean field dynamo theory and accretion disc theory
NASA Astrophysics Data System (ADS)
Blackman, E. G.
2010-01-01
The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.
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.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Splitting fields and general differential Galois theory
Trushin, Dmitry V
2010-11-11
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.
Semiclassical theory of unimolecular dissociation induced by a laser field
NASA Technical Reports Server (NTRS)
Yuan, J.-M.; George, T. F.
1978-01-01
A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.
The tensor hierarchy of 8-dimensional field theories
NASA Astrophysics Data System (ADS)
Andino, Óscar Lasso; Ortín, Tomás
2016-10-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Avoiding Haag's Theorem with Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Ed
2017-03-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.
2015-12-01
payloads on classified host satellites in highly elliptical Molniya orbits. EPS is composed of four segments: the eXtended Data Rate (XDR) Payload...facility, as directed by the Naval Undersea Warfare Center in November 2015. The Time Division Multiple Access Interface Processor , which is the Navy...and data correctness, availability and processing requirements in the Joint integrated architecture. interfaces; services; policy-enforcement
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum simulation of quantum field theories in trapped ions.
Casanova, J; Lamata, L; Egusquiza, I L; Gerritsma, R; Roos, C F; García-Ripoll, J J; Solano, E
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Incorporation of generalized uncertainty principle into Lifshitz field theories
NASA Astrophysics Data System (ADS)
Faizal, Mir; Majumder, Barun
2015-06-01
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Quantum Yang-Mills field theory
NASA Astrophysics Data System (ADS)
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Killing vector fields and harmonic superfield theories
NASA Astrophysics Data System (ADS)
Groeger, Josua
2014-09-01
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Hydrodynamic transport functions from quantum kinetic field theory
NASA Astrophysics Data System (ADS)
Calzetta, E. A.; Hu, B. L.; Ramsey, S. A.
2000-06-01
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with λΦ4 self-interaction we need to include four-loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D 53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear-response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires a clever rendition of diagrammatic resummations which is neither straightforward nor fail-safe. Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-Abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions.
Quantum cellular automata and free quantum field theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
Lattice Study of Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
Winterowd, Christopher; Detar, Carleton; Zafeiropoulos, Savvas
2016-03-01
The discovery of graphene ranks as one of the most important developments in condensed matter physics in recent years. As a strongly interacting system whose low-energy excitations are described by the Dirac equation, graphene has many similarities with other strongly interacting field theories, particularly quantum chromodynamics (QCD). Graphene, along with other relativistic field theories, have been predicted to exhibit spontaneous symmetry breaking (SSB) when an external magnetic field is present. Using nonperturbative methods developed to study QCD, we study the low-energy effective field theory (EFT) of graphene subject to an external magnetic field. We find strong evidence supporting the existence of SSB at zero-temperature and characterize the dependence of the chiral condensate on the external magnetic field. We also present results for the mass of the Nambu-Goldstone boson and the dynamically generated quasiparticle mass that result from the SSB.
Screening of scalar fields in Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Burrage, Clare; Khoury, Justin
2014-07-01
We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.
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.
Using Self Consistent Field Theory on Polymeric Mixtures
NASA Astrophysics Data System (ADS)
von Konigslow, Kier; Park, Chul; Thompson, Russell
The ability to predict the solubility of a particular solvent in a polymer fluid is essential to the production of polymer foams. For the past 40 years, the primary model employed to this end has been an expansion of Flory-Huggins lattice fluid theory developed by Sanchez and Lacombe (S-L theory). S-L theory, while useful in the uniform limit, is limited to homogeneous systems. Self-Consistent Field Theory (SCFT), which has long been in use in polymer physics, is a mean-field theory capable of modeling the equilibrium behaviour of both homogeneous and inhomogeneous systems. We are investigating whether SCFT, applied to polymer-solvent mixtures, is in agreement with SL-theory in the homogeneous limit. Should this prove successful, we hope to use SCFT to model more general mixtures, including inhomogeneous nanocellular polymer foam systems.
On the global symmetries of 6D superconformal field theories
NASA Astrophysics Data System (ADS)
Bertolini, Marco; Merkx, Peter R.; Morrison, David R.
2016-07-01
We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
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
Torque anomaly in quantum field theory
NASA Astrophysics Data System (ADS)
Fulling, S. A.; Mera, F. D.; Trendafilova, C. S.
2013-02-01
The expectation values of energy density and pressure of a quantum field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch-Candelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
Exotic dual of type II double field theory
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Hohm, Olaf; Riccioni, Fabio
2017-04-01
We perform an exotic dualization of the Ramond-Ramond fields in type II double field theory, in which they are encoded in a Majorana-Weyl spinor of O (D , D). Starting from a first-order master action, the dual theory in terms of a tensor-spinor of O (D , D) is determined. This tensor-spinor is subject to an exotic version of the (self-)duality constraint needed for a democratic formulation. We show that in components, reducing O (D , D) to GL (D), one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory.
Constrained field theories on spherically symmetric spacetimes with horizons
NASA Astrophysics Data System (ADS)
Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman
2017-02-01
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.
Field theories and exact stochastic equations for interacting particle systems
Andreanov, Alexei; Lefevre, Alexandre; Biroli, Giulio; Bouchaud, Jean-Philippe
2006-09-15
We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the 'imaginary' Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit.
An extremal $${\\mathcal{N}}=2$$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; ...
2015-11-16
Here, we provide an example of an extremal chiralmore » $${\\mathcal{N}}$$ = 2 superconformal field theory at c = 24. The construction is based on a $${{\\mathbb{Z}}}_{2}$$ orbifold of the theory associated to the $${A}_{1}^{24}$$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.« less
An extremal ${\\mathcal{N}}=2$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiral ${\\mathcal{N}}$ = 2 superconformal field theory at c = 24. The construction is based on a ${{\\mathbb{Z}}}_{2}$ orbifold of the theory associated to the ${A}_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
Holographic thermal field theory on curved spacetimes
NASA Astrophysics Data System (ADS)
Marolf, Donald; Rangamani, Mukund; Wiseman, Toby
2014-03-01
The AdS/CFT correspondence relates certain strongly-coupled CFTs with large effective central charge ceff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly-coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma-balls, which become stable at large ceff. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Non-perturbative methods in relativistic field theory
Franz Gross
2013-03-01
This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.
Localization and Dualities in Three-dimensional Superconformal Field Theories
NASA Astrophysics Data System (ADS)
Willett, Brian
In this thesis we apply the technique of localization to three-dimensional N = 2 superconformal field theories. We consider both theories which are exactly superconformal, and those which are believed to flow to nontrivial superconformal fixed points, for which we consider implicitly these fixed points. We find that in such theories, the partition function and certain supersymmetric observables, such as Wilson loops, can be computed exactly by a matrix model. This matrix model consists of an integral over g , the Lie algebra of the gauge group of the theory, of a certain product of 1-loop factors and classical contributions. One can also consider a space of supersymmetric deformations of the partition function corresponding to the set of abelian global symmetries. In the second part of the thesis we apply these results to test dualities. We start with the case of ABJM theory, which is dual to M-theory on an asymptotically AdS4 x S7 background. We extract strong coupling results in the field theory, which can be compared to semiclassical, weak coupling results in the gravity theory, and a nontrivial agreement is found. We also consider several classes of dualities between two three-dimensional field theories, namely, 3D mirror symmetry, Aharony duality, and Giveon-Kutasov duality. Here the dualities are typically between the IR limits of two Yang-Mills theories, which are strongly coupled in three dimensions since Yang-Mills theory is asymptotically free here. Thus the comparison is again very nontrivial, and relies on the exactness of the localization computation. We also compare the deformed partition functions, which tests the mapping of global symmetries of the dual theories. Finally, we discuss some recent progress in the understanding of general three-dimensional theories in the form of the F-theorem, a conjectured analogy to the a-theorem in four dimensions and c-theorem in two dimensions, which is closely related to the localization computation.
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).
Selected engineering properties and applications of EPS geofoam
NASA Astrophysics Data System (ADS)
Elragi, Ahmed Fouad
Expanded polystyrene (EPS) geofoam is a lightweight material that has been used in engineering applications since at least the 1950s. Its density is about a hundredth of that of soil. It has good thermal insulation properties with stiffness and compression strength comparable to medium clay. It is utilized in reducing settlement below embankments, sound and vibration damping, reducing lateral pressure on substructures, reducing stresses on rigid buried conduits and related applications. This study starts with an overview on EPS geofoam. EPS manufacturing processes are described followed by a review of engineering properties found in previous research work done so far. Standards and design manuals applicable to EPS are presented. Selected EPS geofoam-engineering applications are discussed with examples. State-of-the-art of experimental work is done on different sizes of EPS specimens under different loading rates for better understanding of the behavior of the material. The effects of creep, sample size, strain rate and cyclic loading on the stress strain response are studied. Equations for the initial modulus and the strength of the material under compression for different strain rates are presented. The initial modulus and Poisson's ratio are discussed in detail. Sample size effect on creep behavior is examined. Three EPS projects are shown in this study. The creep behavior of the largest EPS geofoam embankment fill is shown. Results from laboratory tests, mathematical modeling and field records are compared to each other. Field records of a geofoam-stabilized slope are compared to finite difference analysis results. Lateral stress reduction on an EPS backfill retaining structure is analyzed. The study ends with a discussion on two promising properties of EPS geofoam. These are the damping ability and the compressibility of this material. Finite element analysis, finite difference analysis and lab results are included in this discussion. The discussion with the
X(3872) in Effective Field Theory
Fleming, S.; Mehen, T.
2009-12-17
If the X(3872) resonance is a shallow boundstate of a the charm mesons D{sup 0}D-bar*{sup 0} and D*{sup 0}D-bar{sup 0}, it can be described by an effective theory of nonrelativistic D mesons coupled to nonrelativistic pions (X-EFT). In this talk, I give a brief overview of the X(3872), followed by a short review of X-EFT. I end my talk with results from calculations of the the next-to-leading-order correction to the partial decay width {gamma}[X{yields}D{sup 0}D-bar{sup 0}{pi}{sup 0}], and the decay of X(3872) to P-wave quarkonia.
Radiation reaction in quantum field theory
NASA Astrophysics Data System (ADS)
Higuchi, Atsushi
2002-11-01
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant α and in the small ħ approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit.
EPS (Electric Particulate Suspension) Microgravity Technology Provides NASA with New Tools
NASA Technical Reports Server (NTRS)
Colver, Gerald M.; Greene, Nate; Xu, Hua
2004-01-01
The Electric Particulate Suspension is a fire safety ignition test system being developed at Iowa State University with NASA support for evaluating combustion properties of powders, powder-gas mixtures, and pure gases in microgravity and gravitational atmospheres (quenching distance, ignition energy, flammability limits). A separate application is the use of EPS technology to control heat transfer in vacuum and space environment enclosures. In combustion testing, ignitable powders (aluminum, magnesium) are introduced in the EPS test cell and ignited by spark, while the addition of inert particles act as quenching media. As a combustion research tool, the EPS method has potential as a benchmark design for quenching powder flames that would provide NASA with a new fire safety standard for powder ignition testing. The EPS method also supports combustion modeling by providing accurate measurement of flame-quenching distance as an important parameter in laminar flame theory since it is closely related to characteristic flame thickness and flame structure. In heat transfer applications, inert powder suspensions (copper, steel) driven by electric fields regulate heat flow between adjacent surfaces enclosures both in vacuum (or gas) and microgravity. This simple E-field control can be particularly useful in space environments where physical separation is a requirement between heat exchange surfaces.
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.
Statistical field theory description of inhomogeneous polarizable soft matter
NASA Astrophysics Data System (ADS)
Martin, Jonathan M.; Li, Wei; Delaney, Kris T.; Fredrickson, Glenn H.
2016-10-01
We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.
Very special relativity as a background field theory
NASA Astrophysics Data System (ADS)
Ilderton, Anton
2016-08-01
We consider violation of Lorentz invariance in QED induced by a very high frequency background wave. An effective theory is obtained by averaging observables over the rapid field oscillations. This preserves Ward identities and restores translation invariance below the high-frequency scale, but only partial Lorentz invariance: we show that the effective theory is C-invariant SIM(2)-QED in very special relativity. Averaging leads to the nonlocal terms familiar from SIM(2) theories, while the short-distance behavior of the background field fermion propagator generates the infinite number of higher-order vertices of SIM(2)-QED.
Towards field theory in spaces with multivolume junctions
NASA Astrophysics Data System (ADS)
Fomin, P. I.; Shtanov, Yu V.
2002-06-01
We consider a spacetime formed by several pieces with common timelike boundary which plays the role of a junction between them. We establish junction conditions for fields of various spins and derive the resulting laws of wave propagation through the junction, which turn out to be quite similar for fields of all spins. As an application, we consider the case of multivolume junctions in four-dimensional spacetime that may arise in the context of the theory of quantum creation of a closed universe on the background of a big mother universe. The theory developed can also be applied to braneworld models and to the superstring theory.
Fundamental string solutions in open string field theories
Michishita, Yoji
2006-02-15
In Witten's open cubic bosonic string field theory and Berkovits' superstring field theory we investigate solutions of the equations of motion with appropriate source terms, which correspond to Callan-Maldacena solution in Born-Infeld theory representing fundamental strings ending on the D-branes. The solutions are given in order by order manner, and we show some full order properties in the sense of {alpha}{sup '} expansion. In superstring case we show that the solution is 1/2 BPS in full order.
An action for F-theory: {SL}(2){{{R}}}^{+} exceptional field theory
NASA Astrophysics Data System (ADS)
Berman, David S.; Blair, Chris D. A.; Malek, Emanuel; Rudolph, Felix J.
2016-10-01
We construct the 12-dimensional exceptional field theory (EFT) associated to the group {SL}(2)× {{{R}}}+. Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus {SL}(2)× {{{R}}}+ EFT contains both F-theory and M-theory in a single 12-dimensional formalism.
Field theory on R×S 3 topology. V: SU 2 gauge theory
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-02-01
A gauge theory on R×S 3 topology is developed. It is a generalization to the previously obtained field theory on R×S 3 topology and in which equations of motion were obtained for a scalar particle, a spin one-half particle, the electromagnetic field of magnetic moments, and a Shrödinger-type equation, as compared to ordinary field equations defined on a Minkowskian manifold. The new gauge field equations are presented and compared to the ordinary Yang-Mills field equations, and the mathematical and physical differences between them are discussed.
Effective Field Theories from Soft Limits of Scattering Amplitudes.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-05
We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
On classification of extremal non-holomorphic conformal field theories
NASA Astrophysics Data System (ADS)
Tener, James E.; Wang, Zhenghan
2017-03-01
Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category C and a central charge c. A long-term goal is to classify unitary rational conformal field theories based on a classification of unitary modular tensor categories. We conjecture that for any unitary modular tensor category C , there exists a unitary chiral conformal field theory V so that its modular tensor category {{C}V} is C . In this paper, we initiate a mathematical program in and around this conjecture. We define a class of extremal vertex operator algebras with minimal conformal dimensions as large as possible for their central charge, and non-trivial representation theory. We show that there are finitely many different characters of extremal vertex operator algebras V possessing at most three different irreducible modules. Moreover, we list all of the possible characters for such vertex operator algebras with c≤slant 48 .
Comments on conformal Killing vector fields and quantum field theory
Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.
1982-10-15
We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space.
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Topics in lattice QCD and effective field theory
NASA Astrophysics Data System (ADS)
Buchoff, Michael I.
Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (chiPT), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice chiPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 pipi scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Spinor field theory at finite temperature in the early Universe
NASA Astrophysics Data System (ADS)
Banerjee, N.; Mallik, S.
1992-01-01
We consider the Dirac field on a spatially flat Robertson-Walker space-time. We find the exact expression for the Dirac propagator for an arbitrary scale factor in the real-time formulation of finite-temperature field theory. The mode functions used in the construction satisfy uncoupled ordinary differential equations.
Medical Argument and Field Theory: The Laetrile Case.
ERIC Educational Resources Information Center
Dunbar, Nancy R.
One approach to field theory in argumentation begins with a description of argumentation and, by identifying similarities or regularities in discursive practice, attempts to induce the nature and characteristics of a field. The controversy surrounding the use of Laetrile, a proposed cancer treatment, provides an example of this approach. Assuming…
Hermeneutical Field Theory and the Structural Character of Understanding.
NASA Astrophysics Data System (ADS)
Whitehouse, William Leonard
Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints and degrees of freedom that constitute the structural character of understanding. However, as is sometimes the case with their quantitative mathematical counterparts, the hermeneutical field equations are capable of giving a variety of descriptions or solutions for one and the same set of conditions. The task, therefore, is to try to sort out those solutions which have reflective properties with respect to the structural character of reality from those which do not have such properties. The thesis addresses this task by introducing the idea of hermeneutical field theory. In this theory the notion of a semiotic operator or semiotic quantum plays a central role. More specifically, this quantum is considered to be the carrier of hermeneutical force. It arises as a field property at the complex, horizontal membrane-manifold linking human consciousness with different levels of scale of reality. When taken collectively, the aforementioned set of equations gives expression to the structural character of hermeneutical field theory. Therefore, when one begins to run concrete variables through the theory underlying these equations, one encounters various kinds of hermeneutical constraints and degrees of freedom. These constraints and degrees of freedom characterize the dialectical engagement of consciousness and reality as one seeks to acquire understanding concerning the above mentioned variables and the context which gives rise to them. Hermeneutical field theory is really the study of the factors that affect the state of the six internal
New dynamical mean-field dynamo theory and closure approach.
Blackman, Eric G; Field, George B
2002-12-23
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.
Cold atom simulation of interacting relativistic quantum field theories.
Cirac, J Ignacio; Maraner, Paolo; Pachos, Jiannis K
2010-11-05
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
Generalized conservation laws in non-local field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Symmetries in Three-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
Bashkirov, Denis
Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ≥ 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Renormalization and non-linear symmetries in quantum field theory
NASA Astrophysics Data System (ADS)
Velenich, Andrea
Most of the phenomena we experience, from the microscopic world to the universe at its largest scales, are out of equilibrium and their comprehensive formalization is one of the open problems in theoretical physics. Fluids of interacting particles cooled down or compressed quickly enough to become amorphous solids are an example of rich out-of-equilibrium systems with very slow relaxation dynamics. Even though the equilibrium phases are ordered, these systems remain trapped in glassy metastable states, with disordered microscopic structures. As a realistic model of this phenomenology, in the first part of this work I focused on a field theory of particles obeying a Brownian dynamics. The field-theoretic action displays a time-reversal symmetry leading to Fluctuation-Dissipation relations. For non-interacting particles I solved the field theory exactly, providing the explicit form of all the correlation functions, with their space and time dependence. As a non-perturbative result, the distribution of the density field has been proven to be Poissonian and not Gaussian. For interacting particles the field theory presents two major challenges: its apparent non-renormalizability and a non-linear implementation of the time-reversal symmetry. Non-linear field redefinitions can be used to make the symmetry linear and might even lead to the solution of the interacting equations of motion. However they also alter the renormalizability properties of a field theory. These challenges inspired the second part of the work, where a more abstract approach was taken. Using algebraic methods I investigated the effect of non-linear field redefinitions both on symmetry and on renormalization by focusing on simple scalar field theories as toy models. In the formal setting of the Hopf algebra of Feynman diagrams, symmetries take the form of Hopf ideals and enforce relations among scattering amplitudes; such relations can drastically reduce the number of independent couplings in a field
Relating the archetypes of logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-07-01
Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=-2 triplet model, the Wess-Zumino-Witten model on SL(2;R) at level k=-1/2 >, and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and -1/2 >. The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought.
Chiral orbifold construction of field theories with extra dimensions
NASA Astrophysics Data System (ADS)
Hailu, Girma
We build higher dimensional field theories which have chiral fermion zero-modes on orbifolds. We show that orbifold boundary conditions and scalar vacuum expectation values interplay to produce chiral fermions localized on fat three branes. We develop a scheme for computing field propagators in higher dimensional theories obeying chiral orbifold boundary conditions. Using this scheme we compute the loop corrections to an effective field theory in five dimensions. We find that the renormalization group running of the higher dimensional bulk theory leads to a running of the four dimensional brane couplings. We generalize an argument to verify that the chiral anomaly that arises in these chiral orbifold theories is entirely confined on and uniformly distributed over the fixed points of the orbifold, independent of the shape of the chiral zero-modes. We construct a setup in which a scalar field with appropriate profile in the extra dimension is used to address the hierarchy problem and also localize both chiral fermions and zero-mode gravitons on the same three brane in five dimensions. We construct exact and nonpetrurbative quantum moduli spaces and dynamical superpotentials of an infinite set of linear and ring N = 1 supersymmetric moose theories with SU(2) gauge group at each node and link chiral superfields in the fundamental representation.
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
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.
Thermofield dynamics extension of the open string field theory
NASA Astrophysics Data System (ADS)
Botta Cantcheff, M.; Scherer Santos, R. J.
2016-03-01
We study the application of the rules of thermofield dynamics (TFD) to the covariant formulation of open-string field theory. We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended Becchi, Rouet, Stora and Tyutin (BRST) charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement, and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it of which the results at tree level agree with those of the conventional theory.
World sheet commuting {beta}{gamma} conformal field theory and nonrelativistic string theories
Kim, Bom Soo
2007-11-15
We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri [J. Math. Phys. (N.Y.) 42, 3127 (2001)] and Danielsson et al. [J. High Energy Phys. 10 (2000) 020; J. High Energy Phys. 03 (2001) 041.]. Our theory is much simpler than their theory and does not assume a compact coordinate. This nonrelativistic string theory has a bosonic matter {beta}{gamma} conformal field theory with the conformal weight of {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {gamma} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {gamma} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a nonrelativistic dispersion relation without a nontrivial topology in the nonrelativistic setup, which is one of the major differences from the previous works of Gomis and Ooguri and of Danielsson and co-workers. This simple theory is the nonrelativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} conformal field theory. We also mention supersymmetric generalizations of these theories.
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.
Inductive approach towards a phenomenologically more satisfactory unififed field theory
Rayski, J.; Rayski J.M. Jnr.
1985-11-01
A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.
Theory of Near-Field Scanning with a Probe Array
2014-01-01
NF samples are then processed to produce FF patterns. The processing, known as the NF-to-FF transformation [1][2], is exact and rigorous in that, if...location and is a critical input to the NF-to-FF transformation . The expansion coefficients b(−) of the total outgoing field determines the extent of...of error, we provided a probe array compensation theory based on the Lorentz reciprocity theorem [29]. The theory permits expression of the open
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Quantum field theory on curved spacetimes: Axiomatic framework and examples
NASA Astrophysics Data System (ADS)
Fredenhagen, Klaus; Rejzner, Kasia
2016-03-01
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
Chiral Effective Field Theory in the $\\Delta$-resonance region
Vladimir Pascalutsa
2006-09-18
I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the $\\Delta(1232)$, the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the $\\Delta$-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Motion of small bodies in classical field theory
Gralla, Samuel E.
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
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.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
Quantum Entanglement of Local Operators in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-01
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
A Variational Statistical-Field Theory for Polar Liquid Mixtures
NASA Astrophysics Data System (ADS)
Zhuang, Bilin; Wang, Zhen-Gang
Using a variational field-theoretic approach, we derive a molecularly-based theory for polar liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy of mixing and the dielectric constant as functions of mixture composition. Using only the dielectric constants and the molar volumes of the pure liquid constituents, the theory evaluates the mixture dielectric constants in good agreement with the experimental values for a wide range of liquid mixtures, without using adjustable parameters. In addition, the theory predicts that liquids with similar dielectric constants and molar volumes dissolve well in each other, while sufficient disparity in these parameters result in phase separation. The calculated miscibility map on the dielectric constant-molar volume axes agrees well with known experimental observations for a large number of liquid pairs. Thus the theory provides a quantification for the well-known empirical ``like-dissolves-like'' rule. Bz acknowledges the A-STAR fellowship for the financial support.
Continuous-spin particle field theory with helicity correspondence
NASA Astrophysics Data System (ADS)
Schuster, Philip; Toro, Natalia
2015-01-01
We propose the first covariant local action describing the propagation of a single free continuous-spin degree of freedom. The theory is simply formulated as a gauge theory in a "vector superspace," but can also be formulated in terms of a tower of symmetric tensor gauge fields. When the spin invariant ρ vanishes, the helicity correspondence is manifest—familiar gauge theory actions are recovered and couplings to conserved currents can easily be introduced. For nonzero ρ , a tower of tensor currents must be present, of which only the lowest rank is exactly conserved. A paucity of local gauge-invariant operators for nonzero ρ suggests that the equations of motion in any interacting theory should be covariant, not invariant, under a generalization of the free theory's gauge symmetry.
Entanglement entropy of non-unitary conformal field theory
NASA Astrophysics Data System (ADS)
Bianchini, D.; Castro-Alvaredo, O.; Doyon, B.; Levi, E.; Ravanini, F.
2015-01-01
Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as {{S}n}˜ \\frac{{{c}eff}(n+1)}{6n}log \\ell , where {{c}eff}=c-24Δ \\gt 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Δ \
Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories.
Sulejmanpasic, Tin
2017-01-06
We discuss quantum field theories with global SU(N) and O(N) symmetries for which temporal direction is compactified on a circle of size L with periodicity of fields up to a global symmetry transformation, i.e., twisted boundary conditions. Such boundary conditions correspond to an insertion of the global symmetry operator in the partition function. We argue in general and prove in particular for CP(N-1) and O(N) nonlinear sigma models that large-N volume independence holds. Further we show that the CP(N-1) theory is free from the Affleck phase transition confirming the Ünsal-Dunne continuity conjecture.
Mapping a Massless Scalar Field Theory on a Yang-Mills Theory:. Classical Case
NASA Astrophysics Data System (ADS)
Frasca, Marco
We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.
A field theory of piezoelectric media containing dislocations
Taupin, V. Fressengeas, C.; Ventura, P.; Lebyodkin, M.
2014-04-14
A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.
Preheating in an asymptotically safe quantum field theory
NASA Astrophysics Data System (ADS)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-10-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance instability in the production of these fields, and the danger that the induced curvature fluctuations will become too large. Here we show that the parametric instability indeed arises, and that hence the energy transfer from the inflaton condensate to fluctuating fields is rapid. Demanding that the curvature fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e -foldings of the inflationary phase.
The Role of Healthcare Providers in the Roll-Out of PrEP
Krakower, Douglas S.; Mayer, Kenneth H.
2015-01-01
Purpose of Review To review the most recent studies assessing the preparedness of healthcare practitioners to provide anti-HIV pre-exposure prophylaxis (PrEP) and to suggest areas for future implementation research. Recent Findings As PrEP is a bio-behavioral intervention, healthcare providers are likely to play a critical role in implementing PrEP in care settings. Studies suggest that many specialized providers are aware of PrEP and support its provision as a public health intervention, though knowledge and acceptance are less among generalists. Therefore, utilization of PrEP by clinicians has been limited to a few early adopters. Concerns about the efficacy and long-term safety of PrEP, and perceived barriers to prescribing PrEP, could limit prescribing behaviors and intentions. Resistance to performing routine HIV risk assessments by clinicians is an additional barrier to implementing PrEP, though innovative tools to help clinicians routinely perform risk assessments are being developed. Summary Interventions are needed to engage a broader array of healthcare providers in PrEP provision. Utilizing a framework based on diffusion of innovation theory, this review proposes strategies that can be implemented and evaluated to increase PrEP prescribing by healthcare providers. If resources are invested in training clinicians to provide PrEP, then these stakeholders could enhance the use of PrEP as part of a prevention package by primary providers. PMID:26417953
Soto, Ana M.; Sonnenschein, Carlos
2014-01-01
The somatic mutation theory (SMT) of cancer has been and remains the prevalent theory attempting to explain how neoplasms arise and progress. This theory proposes that cancer is a clonal, cell-based disease, and implicitly assumes that quiescence is the default state of cells in multicellular organisms. The SMT has not been rigorously tested, and several lines of evidence raise questions that are not addressed by this theory. Herein, we propose experimental strategies that may validate the SMT. We also call attention to an alternative theory of carcinogenesis, the tissue organization field theory (TOFT), which posits that cancer is a tissue-based disease and that proliferation is the default state of all cells. Based on epistemological and experimental evidence, we argue that the TOFT compellingly explains carcinogenesis, while placing it within an evolutionarily relevant context. PMID:21503935
Lattice field theory studies of magnetic catalysis in graphene
NASA Astrophysics Data System (ADS)
Winterowd, Christopher R.
Consisting of a single two-dimensional layer of Carbon atoms arranged in a hexagonal lattice, graphene represents one of the most exciting recent developments in condensed matter physics. With novel electronic and mechancial properties, graphene not only has great potential with respect to technological applications, but also displays phenomena that typically appear in relativistic quantum field theory. The low-energy electronic excitations of graphene consist of two identical species of massless Dirac particles. Due to the small Fermi velocity, these particles are strongly coupled through the Coulomb interaction. Although various perturbative approaches have succeeded in elucidating many of the electronic properties of graphene, one would still like a nonperturbative study to address various questions. In particular, the spontaneous breaking of chiral symmetry in the presence of an external magnetic field, commonly known as magnetic catalysis, is one of these questions. Early studies of this phenomenon in model relativistic field theories have posited the mechanism to be universal. More recently, this mechanism of spontaneous symmetry breaking has been studied in low-dimensional condensed matter systems. Due to the strongly-coupled nature of the low-energy effective field theory of graphene, nonperturbative methods of lattice gauge theory can be used which are well suited to studying chiral symmetry breaking. Most notably used to study the theory of the strong interactions, quantum chromodynamics, these methods have proven successful in elucidating nonperturbative phenomena in cases where perturbative methods fail. In this thesis, using these methods, evidence in favor of magnetic catalysis in the graphene effective field theory will be presented.
Fuzzy Field Theory as a Random Matrix Model
NASA Astrophysics Data System (ADS)
Tekel, Juraj
This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices. First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables. We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case. Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Aspects of Supersymmetric Field Theories and Complex Geometry
NASA Astrophysics Data System (ADS)
Crichigno, Patricio Marcos
In this dissertation we study various aspects of Supersymmetric Quantum Field Theory and Complex Geometry. We focus on three main aspects. The first is general N = (2, 2) gauged linear sigma models involving semichiral fields. We show that integrating out the semichiral vector multiplet leads to the generalized potential for a hyperkahler manifold, providing a formulation of the hyperkahler quotient in a generalized setting. We then discuss a new quotient construction which leads to non-Kahler manifolds. The second problem we study is motivated by recent developments in the study of the Coulomb branch of supersymmetric theories with a hyperkahler moduli space. A crucial element in these developments is the expression for Darboux coordinates in the hyperkahler manifold. We give a simple derivation of this expression by using projective superspace techniques and we apply this to the study of the moduli space of theories with eight supercharges on R3 x S¹ and R3 x T². Finally, we study the partition function of three-dimensional Chern-Simons theories on S³ with affine ADE quivers. We give a general formula for the partition function of affine D-type quivers in terms of the Chern-Simons levels, providing a prediction for the volume of an infinite family of tri-Sasaki Einstein manifolds corresponding to the gravitational duals of such field theories.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
NASA Astrophysics Data System (ADS)
Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, René; Park, Jeong-Hyuck
2015-12-01
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
Positive Energy Conditions in 4D Conformal Field Theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus; Prilepina, Valentina
2016-03-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality avgT00 >= - C /L4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the ``conformal collider'' constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
Dirac's equation and the nature of quantum field theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2012-11-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
ERIC Educational Resources Information Center
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…
NASA Astrophysics Data System (ADS)
Goncharov, Yu. P.
This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.
G{sub Ep}/G{sub Mp} ratio by polarization transfer in ep {yields} ep
Mark K. Jones; Konrad A. Aniol; F.T. Baker; J. Berthot; Pierre Bertin; William Bertozzi; A. Besson; Louis Bimbot; Werner Boeglin; Ed Brash; D. Brown; John Calarco, Larry S. Cardman; C.-C. Chang; Jian-ping Chen; Eugene Chudakov; Steve Churchwell; Evaristo Cisbani; Dan Dale; R. De Leo; Alexandre Deur; Brian Diederich; John Domingo; Martin B. Epstein; Lars Ewell; Kevin Fissum; A. Fleck; Helene Fonvieille; Salvatore Frullani; J. Gao; Franco Garibaldi; Ashot Gasparian; G. Gerstner; Shalev Gilad; Ron Gilman.; Alexander Glamazdin; Charles Glashausser; Javier Gomez; V. Gorbenko; A. Green; Jens-Ole Hansen; Howell, C.R.; Huber, G.M.; Mauro Iodice; Kees de Jager; Stephanie Jaminion; Xiangdong Jiang; William Kahl; James J. Kelly; M. Khayat; Laird H. Kramer; G. Kumbartzki; Michael Kuss; E. Lakuriki; G. Lavessiere; John J. LeRose; Meme Liang; Richard Lindgren; Nilanga Liyanage; George Lolos; R. Macri; Richard Madey; Sergey Malov; Dimitri Margaziotis; Pete Markowitz; Kathy McCormick; Justin McIntyre; R.L. van der Meer; R. Michaels; B.D. Milbrath; Jean Mougey; S.K. Nanda; E.A.J.M. Offerman; Z. Papandreou; Charles F. Perdrisat; Gerassimos G. Petratos; N.M. Piskunov; R.I. Pomatsalyuk; David Prout; Vina Punjabi; Gilles Quemener; Ronald Ransome; Brian Raue; Yves Roblin; Rikki Roche; Gary Rutledge; Paul Rutt; Arun Saha; Teijiro Saito; Adam Sarty; Timothy Smith; P. Sorokin; Steffen Strauch; R. Suleiman; K. Takahashi; Jeff Templon; Luminita Todor; Paul E. Ulmer; Guido M. Urciuoli; Pascal Vernin; B. Vlahovic; H. Voskanyan, H.; Krishni Wijesooriya; Bogdan Wojtsekhowski; R.J. Woo; F. Xiong; George Dan Zainea; Z.-L. Zhou
2000-02-14
The ratio of the proton's elastic electromagnetic form factors, G{sub Ep}/G{sub Mp} was obtained by measuring P{sub t} and P{ell}, the transverse and the longitudinal recoil proton polarization, respectively. For elastic ep {yields} ep, G{sub Ep}/G{sub Mp} is proportional to P{sub t}/P{ell}. Simultaneous measurement of P{sub t} and P{ell} in a polarimeter provides good control of the systematic uncertainty. The results for the ratio G{sub Ep}/G{sub Mp} show a systematic decrease as Q{sup 2} increases from 0.5 to 3.5 GeV{sup 2}, indicating for the first time a definite difference in the spatial distribution of charge and magnetization currents in the proton.
Decoherence in an interacting quantum field theory: The vacuum case
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2010-03-15
We apply the decoherence formalism to an interacting scalar field theory. In the spirit of the decoherence literature, we consider a 'system field' and an 'environment field' that interact via a cubic coupling. We solve for the propagator of the system field, where we include the self-energy corrections due to the interaction with the environment field. In this paper, we consider an environment in the vacuum state (T=0). We show that neglecting inaccessible non-Gaussian correlators increases the entropy of the system as perceived by the observer. Moreover, we consider the effect of a changing mass of the system field in the adiabatic regime, and we find that at late times no additional entropy has been generated.
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
On gradient field theories: gradient magnetostatics and gradient elasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2014-09-01
In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot-Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach-Koehler stress equation, Peach-Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.
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.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories.
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F
2017-03-10
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS_{6}×S^{2} warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p,q) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F.
2017-03-01
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6×S2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p ,q ) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Information channel capacity in the field theory estimation
NASA Astrophysics Data System (ADS)
Sładkowski, J.; Syska, J.
2012-12-01
The construction of the information capacity for the vector position parameter in the Minkowskian space-time is presented. This lays the statistical foundations of the kinematical term of the Lagrangian of the physical action for many field theory models, derived by the extremal physical information method of Frieden and Soffer.
The effective field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg00(u))n at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
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.
Effective field theory for plasmas at all temperatures and densities
NASA Astrophysics Data System (ADS)
Braaten, Eric
1993-05-01
The solution of the plasmon problem and the subsequent development of an effective field-theory approach to ultrarelativistic plasmas are reviewed. The effective Lagrangians that summarize collective effects in ultrarelativistic quark-gluon and electron-photon plasmas are presented. A generalization that describes an electromagnetic plasma at all temperatures and densities is proposed.
Recent Progress in Nuclear Lattice Simulations with Effective Field Theory
NASA Astrophysics Data System (ADS)
Lee, D.
2007-10-01
This proceedings article summarizes recent work presented at Chiral Dynamics 2006 on nuclear lattice simulations with chiral effective field theory for light nuclei. This work has been done in collaboration with Bubar {gra} Borasoy , Evgeny Epelbaum, Hermann Krebs, and Ulf-G. Meißner.
Constructive field theory and applications: Perspectives and open problems
NASA Astrophysics Data System (ADS)
Rivasseau, V.
2000-06-01
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with constructive methods well into the 21st century.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Chiral field theories as models for hadron substructure
Kahana, S.H.
1987-03-01
A model for the nucleon as soliton of quarks interacting with classical meson fields is described. The theory, based on the linear sigma model, is renormalizable and capable of including sea quarks straightforwardly. Application to nuclear matter is made in a Wigner-Seitz approximation.
Sketch of J. R. Kantor's Psychological Interbehavioral Field Theory
ERIC Educational Resources Information Center
Delprato, Dennis J.; Smith, Noel W.
2009-01-01
We provide a sketch of J. R. Kantor's (1959, 1971) psychological interbehavioral field (IBF) theory by identifying 9 essential points and briefly discussing each. The main emphasis of this sketch is on the foundation of Kantor's thinking, the IBF. Suggestions for further study are provided.
Quantum Corrections and Effective Action in Field Theory
NASA Astrophysics Data System (ADS)
Dalvit, Diego A. R.
1998-07-01
In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We introduce a coarse grained effective action, which is useful in the study of phase transitions in field theory. We derive an exact renormalization group equation that describes how this action varies with the coarse graining scale. We develop different approximation methods to solve that equation, and we obtain non perturbative improvements to the effective potential for a self interacting scalar field theory. We also discuss the stochastic aspects contained in this action. On the other hand, using the effective action, we find low energy and large distance quantum corrections for the gravitational potential, treating relativity as an effective low energy theory. We include the effect of scalar fields, fermions and gravitons. The inclusion of metric fluctuations causes Einstein semiclassical equations to depend on the gauge fixing parameters, and they are therefore non physical. We solve this problem identifying as a physical observable the trayectory of a test particle. We explicitly show that the geodesic equation for such particle is independent of the arbitrary parameters of the gauge fixing.
The effective field theory of K-mouflage
Brax, Philippe; Valageas, Patrick E-mail: patrick.valageas@cea.fr
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg{sup 00}{sub (u)}){sup n} at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
Morse theory for vector fields and the Witten Laplacian
Enciso, Alberto; Peralta-Salas, Daniel
2009-05-06
In this paper we informally review some recent developments on the analytical approach to Morse-type inequalities for vector fields. Throughout this work we focus on the main ideas of this approach and emphasize the application of the theory to concrete examples.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
New symbolic tools for differential geometry, gravitation, and field theory
NASA Astrophysics Data System (ADS)
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
Field theory on R× S 3 topology: Lagrangian formulation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malka, A.
1990-01-01
A brief description of the ordinary field theory, from the variational and Noether's theorem point of view, is outlined. A discussion is then given of the field equations of Klein-Gordon, Schrödinger, Dirac, Weyl, and Maxwell in their ordinary form on the Minkowskian space-time manifold as well as on the topological space-time manifold R × S3 as they were formulated by Carmeli and Malin, including the latter's most general solutions. We then formulate the general variational principle in the R × S3 topological space, from which we derive the field equations in this space.
Finite temperature scalar field theory in the early universe
Leutwyler, H.; Mallik, S. )
1991-01-01
The authors study a scalar Higgs field in an expanding Robertson-Walker geometry, using the real time formulation of Semenoff and Weiss. It is shown that the density matrix associated with the Hamiltonian at a sharp time describes a state for which perturbation theory is not renormalizable and an alternative, renormalizable characterization of thermal equilibrium is given. They calculate the thermal quantum fluctuations surrounding a classical field and discuss the characteristic time scales occurring in the evolution of a scalar field from an initial radiation dominated phase of thermal equilibrium to an unstable, inflationary de Sitter phase.
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-15
The ''basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a {phi}{sup 4} interaction to three-loop order. (c) 2000 The American Physical Society.
Microbial extracellular polymeric substances (EPS) in fresh water sediments.
Gerbersdorf, Sabine Ulrike; Westrich, Bernhard; Paterson, David M
2009-08-01
Microbially produced extracellular polymeric substances (EPS) have been linked with many important ecological functions in natural sediments; yet, most information has been derived from marine systems. The present paper is the first comprehensive study on EPS (i.e., carbohydrates and proteins) dynamics in riverine sediments addressing spatial (six reservoirs and four groyne fields across three European rivers), temporal (all seasons in 2003-2005), and vertical (over a 50-cm sediment depth transect) pattern. The variation in hydrodynamic regime found in the reservoirs and groyne fields was reflected in the biomass and composition of the benthic microorganisms that produce EPS. The microphytobenthic communities consisted mainly of diatoms and a higher algal biomass (up to 248 microg g(-1) dry weight, DW) seemed to be indicative for higher amounts of secreted colloidal carbohydrates. Consequently, the model proposed by Underwood and Smith (1998) for the relation chlorophyll-colloidal carbohydrates was also applicable for upper riverine sediment layers. The close relation between algal biomass and bacterial cell counts (10(8)-10(9) cells g(-1) DW) supports the idea of bacterial use of the secreted EPS. However, the data also suggest a contribution to the EPS pool through bacterial secretion of proteins/extracellular enzymes and possibly carbohydrates. Over depth, the relationships between microorganisms and EPS became increasingly decoupled along with increasing ratios of bound (refractory) to colloidal (labile) EPS. These data suggest fresh production of polymeric substances in upper sediment layers and mainly accumulation of refractory, biodegraded material in deeper layers. The high contents of EPS colloidal and bound carbohydrates (0.1-1.8 and 1.3-6.7 mg g(-1) DW, respectively) and EPS proteins (0.4-12.9 mg g(-1) DW) at the freshwater study sites might indicate an important role in sediment ecology.
Universal entanglement spectra of gapped one-dimensional field theories
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Ludwig, Andreas W. W.; Ryu, Shinsei
2017-03-01
We discuss the entanglement spectrum of the ground state of a (1+1)-dimensional system in a gapped phase near a quantum phase transition. In particular, in proximity to a quantum phase transition described by a conformal field theory (CFT), the system is represented by a gapped Lorentz invariant field theory in the "scaling limit" (correlation length ξ much larger than microscopic "lattice" scale "a "), and can be thought of as a CFT perturbed by a relevant perturbation. We show that for such (1+1) gapped Lorentz invariant field theories in infinite space, the low-lying entanglement spectrum obtained by tracing out, say, left half-infinite space, is precisely equal to the physical spectrum of the unperturbed gapless, i.e., conformal field theory defined on a finite interval of length Lξ=ln(ξ /a ) with certain boundary conditions. In particular, the low-lying entanglement spectrum of the gapped theory is the finite-size spectrum of a boundary conformal field theory, and is always discrete and universal. Each relevant perturbation, and thus each gapped phase in proximity to the quantum phase transition, maps into a particular boundary condition. A similar property has been known to hold for Baxter's corner transfer matrices in a very special class of fine-tuned, namely, integrable off-critical lattice models, for the entire entanglement spectrum and independent of the scaling limit. In contrast, our result applies to completely general gapped Lorentz invariant theories in the scaling limit, without the requirement of integrability, for the low-lying entanglement spectrum. While the entanglement spectrum of the ground state of a gapped theory on a finite interval of length 2 R with suitable boundary conditions, bipartitioned into two equal pieces, turns out to exhibit a crossover between the finite-size spectra of the same CFT with in general different boundary conditions as the system size R crosses the correlation length from the "critical regime'' R ≪ξ to the
Pomeron-Odderon interactions in a Reggeon field theory
NASA Astrophysics Data System (ADS)
Bartels, Jochen; Contreras, Carlos; Vacca, Gian Paolo
2017-01-01
In this paper we extend our recent nonperturbative functional renormalization group analysis of Reggeon field theory to the interactions of Pomeron and Odderon fields. We establish the existence of a fixed point and its universal properties, which exhibits a novel symmetry structure in the space of Odderon-Pomeron interactions. As in our previous analysis, this part of our program aims at the investigation of the IR limit of Reggeon field theory (the limit of high energies and large transverse distances). It should be seen in the broader context of trying to connect the nonperturbative infrared region (large transverse distances) with the UV region of small transverse distances where the high energy limit of perturbative QCD applies. We briefly discuss the implications of our findings for the existence of an Odderon in high energy scattering.
Topologically stratified energy minimizers in a product Abelian field theory
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-09-01
We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities
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.
Fang, Yan-Jia; Zhan, Xiao-Qin; Yao, Jin-Jing; Mei, Yan-Ai
2013-01-01
Although the modulation of Ca2+ channel activity by extremely low-frequency electromagnetic fields (ELF-EMF) has been studied previously, few reports have addressed the effects of such fields on the activity of voltage-activated Na+ channels (Nav). Here, we investigated the effects of ELF-EMF on Nav activity in rat cerebellar granule cells (GCs). Our results reveal that exposing cerebellar GCs to ELF-EMF for 10–60 min significantly increased Nav currents (INa) by 30–125% in a time- and intensity-dependent manner. The Nav channel steady-state activation curve, but not the steady-state inactivation curve, was significantly shifted (by 5.2 mV) towards hyperpolarization by ELF-EMF stimulation. This phenomenon is similar to the effect of intracellular application of arachidonic acid (AA) and prostaglandin E2 (PGE2) on INa in cerebellar GCs. Increases in intracellular AA, PGE2 and phosphorylated PKA levels in cerebellar GCs were observed following ELF-EMF exposure. Western blottings indicated that the NaV 1.2 protein on the cerebellar GCs membrane was increased, the total expression levels of NaV 1.2 protein were not affected after exposure to ELF-EMF. Cyclooxygenase inhibitors and PGE2 receptor (EP) antagonists were able to eliminate this ELF-EMF-induced increase in phosphorylated PKA and INa. In addition, ELF-EMF exposure significantly enhanced the activity of PLA2 in cerebellar GCs but did not affect COX-1 or COX-2 activity. Together, these data demonstrate for the first time that neuronal INa is significantly increased by ELF-EMF exposure via a cPLA2 AA PGE2 EP receptors PKA signaling pathway. PMID:23349866
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
Positive energy conditions in 4D conformal field theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus A.; Prilepina, Valentina
2016-10-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality < T 00> ≥ - C/L 4, where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
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.
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.
Power counting and Wilsonian renormalization in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
A tracer-kinetic field theory for medical imaging.
Sourbron, Steven
2014-04-01
Dynamic imaging data are currently analyzed with a tracer-kinetic theory developed for individual time curves measured over whole organs. The assumption is that voxels represent isolated systems which all receive indicator through the same arterial inlet. This leads to well-known systematic errors, but also fails to exploit the spatial structure of the data. In this study, a more general theoretical framework is developed which makes full use of the specific structure of image data. The theory encodes the fact that voxels receive indicator from their immediate neighbors rather than from an upstream arterial input. This results in a tracer-kinetic field theory where the tissue parameters are functions of space which can be measured by analyzing the temporal and spatial patterns in the concentrations. The implications are evaluated through a number of field models for common tissue types. The key benefits of a tracer-kinetic field theory are that: 1) long-standing systematic errors can be corrected, specifically the issue of bolus dispersion and the contamination of large-vessel blood flow on tissue perfusion measurements; 2) additional tissue parameters can be measured that characterize convective or diffusive exchange between voxels; 3) the need to measure a separate arterial input function can be eliminated.
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Lally, Michelle; Zimet, Gregory; Kahn, Jessica A.
2015-01-01
Abstract Prior to issuing formal HIV pre-exposure prophylaxis (PrEP) clinical practice guidelines in 2014, the US Centers for Disease Control and Prevention (CDC) had released interim guidance for oral PrEP use among adults. Because oral PrEP may be used off-label for youth and may soon be indicated for minor adolescents, we examined the potential adoption of the interim guidance among clinicians who care for HIV-infected and at-risk youth. Individual, semi-structured interviews were conducted with 15 US clinicians who were recruited through an adolescent HIV research network. The theory-driven interview guide, consisting primarily of open-ended questions, assessed demographics, familiarity with the guidance, attitudes toward the guidance, and attitudes toward the use of the guidance for adult and adolescent patients. Transcripts were analyzed using framework analysis. Most clinicians (11/15) reported that the guidance was compatible with their practice, although several reported that some aspects, particularly frequency of follow-up visits, needed to be tailored to meet their patients' needs. We found variability in clinician reported characteristics of appropriate PrEP candidates (e.g., youth with substance use and mental health issues were noted to be both suitable and unsuitable PrEP candidates) and PrEP use in serodiscordant couples (e.g., whether PrEP would be recommended to a patient whose HIV-infected partner is virally suppressed). Clinician reported steps for initiation, monitoring, and discontinuing PrEP were largely consistent with the guidance. The observed variability in clinician practice with regard to oral PrEP may be reduced through interventions to educate clinicians about the content and rationale for guideline recommendations. PMID:25692683
Heavy dark matter annihilation from effective field theory.
Ovanesyan, Grigory; Slatyer, Tracy R; Stewart, Iain W
2015-05-29
We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments.
Dynamics of Compact Binaries in Effective Field Theory Formalism
NASA Astrophysics Data System (ADS)
Perrodin, Delphine
2010-02-01
Coalescing compact binaries are predicted to be powerful emitters of gravitational waves, and provide a strong gravity environment ideal for the testing of gravity theories. We study the gravitational dynamics in the early inspiral phase of coalescing compact binaries using Non-Relativistic General Relativity (NRGR) - an effective field theory formalism based on the Post-Newtonian approximation to General Relativity, but which provides a consistent lagrangian framework and a systematic way in which to study binary dynamics and gravitational wave emission. We calculate in this framework the spin-orbit correction to the newtonian potential at 2.5 PN. )
Lagrangian-Hamiltonian unified formalism for field theory
NASA Astrophysics Data System (ADS)
Echeverría-Enríquez, Arturo; López, Carlos; Marín-Solano, Jesús; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
2004-01-01
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations.
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; ...
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power countingmore » is constructed.« less
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; Schiavilla, Rocco; Viviani, Michele
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power counting is constructed.
Nucleon propagation through nuclear matter in chiral effective field theory
NASA Astrophysics Data System (ADS)
Mallik, S.; Mishra, H.
2007-05-01
We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg’s method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature.
Quantum group symmetry of N=1 superconformal field theories
NASA Astrophysics Data System (ADS)
Jiménez, F.
1990-12-01
We use the Gómez-Sierra contour deformation techniques to show that N=1 superconformal field theories with {2c}/{3<1}, in their Coulomb gas version, contain a quantum group structure as an underlying symmetry. In particular, we construct from the thermal subalgebras of these theories, the representation spaces of the quantized universal enveloping superalgebra U q osp(2, 1) and show how to compute its R-matrix, the comultiplication rules and its quantum Clebsch-Gordan coefficients by using a convenient definition of the screened vertex operators and an explicit realization of its generators.
Effective field theory for dilute fermions with pairing
Furnstahl, R.J. Hammer, H.-W. Puglia, S.J.
2007-11-15
Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn-Sham density functional theory (DFT) for medium and heavy nuclei. An effective action formalism for local composite operators leads to a free-energy functional that includes pairing by applying an inversion method order by order in the EFT expansion. A consistent renormalization scheme is demonstrated for the uniform system through next-to-leading order, which includes induced-interaction corrections to pairing.
The principle of stationary variance in quantum field theory
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2014-02-01
The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.
Advanced mean-field theory of the restricted Boltzmann machine
NASA Astrophysics Data System (ADS)
Huang, Haiping; Toyoizumi, Taro
2015-05-01
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.
Large N correlation functions in superconformal field theories
NASA Astrophysics Data System (ADS)
Rodriguez-Gomez, Diego; Russo, Jorge G.
2016-06-01
We compute correlation functions of chiral primary operators in mathcal{N}=2 super-conformal theories at large N using a construction based on supersymmetric localization recently developed by Gerchkovitz et al. We focus on mathcal{N}=4 SYM as well as on supercon-formal QCD. In the case of mathcal{N}=4 we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large N limit. The final correlators admit a simple generalization to a finite N formula which exactly matches the various small N results in the literature.
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.
Chaos and order in non-integrable model field theories
Campbell, D.K.; Peyrard, M.
1989-01-01
We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.
From effective field theories to effective density functionals in and beyond the mean field
NASA Astrophysics Data System (ADS)
Grasso, M.; Lacroix, D.; van Kolck, U.
2016-06-01
Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy-density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.
Discrete field theories and spatial properties of strings
Klebanov, I.; Susskind, L.
1988-10-01
We use the ground-state wave function in the light-cone gauge to study the spatial properties of fundamental strings. We find that, as the cut-off in the parameter space is removed, the strings are smooth and have a divergent size. Guided by these properties, we consider a large-N lattice gauge theory which has an unstable phase where the size of strings diverges. We show that this phase exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero for this equivalence to hold. Thus, exact rotation and translation invariance is restored in a discrete space. This suggests that the number of fundamental short-distance degrees of freedom in string theory is much smaller than in a conventional field theory. 11 refs., 4 figs.
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.
Stochastic Simulation of Microseisms Using Theory of Conditional Random Fields
NASA Astrophysics Data System (ADS)
Morikawa, H.; Akamatsu, J.; Nishimura, K.; Onoue, K.; Kameda, H.
-We examine the applicability of conditional stochastic simulation to interpretation of microseisms observed on soft soil sediments at Kushiro, Hokkaido, Japan. The theory of conditional random fields developed by Kameda and Morikawa (1994) is used, which allows one to perform interpolation of a Gaussian stochastic time-space field that is conditioned by realized values of time functions specified at some discrete locations. The applicability is examined by a blind test, that is, by comparing a set of simulated seismograms and recorded ones obtained from three-point array observa tions. A test of fitness was performed by means of the sign test. It is concluded that the method is applicable to interpretation of microseisms, and that the wave field of microseisms can be treated as Gaussian random fields both in time and space.
Operator Algebras and Noncommutative Geometric Aspects in Conformal Field Theory
NASA Astrophysics Data System (ADS)
Longo, Roberto
2010-03-01
The Operator Algebraic approach to Conformal Field Theory has been particularly fruitful in recent years (leading for example to the classification of all local conformal nets on the circle with central charge c < 1, jointly with Y. Kawahigashi). On the other hand the Operator Algebraic viewpoint offers a natural perspective for a Noncommutative Geometric context within Conformal Field Theory. One basic point here is to uncover the relevant structures. In this talk I will explain some of the basic steps in this "Noncommutative Geometrization program" up to the recent construction of a spectral triple associated with certain Ramond representations of the Supersymmetric Virasoro net. So Alain Connes framework enters into play. This is a joint work with S. Carpi, Y. Kawahigashi, and R. Hillier.
The perturbative structure of spin glass field theory
NASA Astrophysics Data System (ADS)
Temesvári, T.
2014-03-01
Cubic replicated field theory is used to study the glassy phase of the short-range Ising spin glass just below the transition temperature, and for systems above, at, and slightly below the upper critical dimension six. The order parameter function is computed up to two-loop order. There are two, well-separated bands in the mass spectrum, just as in mean field theory. The small mass band acts as an infrared cutoff, whereas contributions from the large mass region can be computed perturbatively (d>6), or interpreted by the ɛ-expansion around the critical fixed point (d=6-ɛ). The one-loop calculation of the (momentum-dependent) longitudinal mass, and the whole replicon sector is also presented. The innocuous behavior of the replicon masses while crossing the upper critical dimension shows that the ultrametric replica symmetry broken phase remains stable below six dimensions.
Shape dependence of entanglement entropy in conformal field theories
NASA Astrophysics Data System (ADS)
Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
2016-04-01
We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R^{1,d-1} . We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ /C_T=π^2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standardmore » operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.« less
The combinatorics of Green's functions in planar field theories
NASA Astrophysics Data System (ADS)
Ebrahimi-Fard, Kurusch; Patras, Frédéric
2016-12-01
The aim of this exposition is to provide a detailed description of the use of combinatorial algebra in quantum field theory in the planar setting. Particular emphasis is placed on the relations between different types of planar Green's functions. The primary object is a Hopf algebra that is naturally defined on variables representing non-commuting sources, and whose coproduct splits into two half-coproducts. The latter give rise to the notion of an unshuffle bialgebra. This setting allows a description of the relation between full and connected planar Green's functions to be given by solving a simple linear fixed point equation. We also include a brief outline of the consequences of our approach in the framework of ordinary quantum field theory.
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
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.
Higher-rank supersymmetric models and topological conformal field theory
NASA Astrophysics Data System (ADS)
Kawai, Toshiya; Uchino, Taku; Yang, Sung-Kil
1993-03-01
In the first part of this paper we investigate the operator aspect of a higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the N = 2 minimal model with the simplest case su(2) corresponding to the N = 2 minimal model. In particular we identify the analogs of chirality conditions and chiral ring. In the second part we construct a class of topological conformal field theories starting with this higher-rank supersymmetric model. We show the BRST-exactness of the twisted stress-energy tensor, find out physical observables and discuss how to make their correlation functions. It is emphasized that in the case of su(2) the topological field theory constructed in this paper is distinct from the one obtained by twisting the N = 2 minimal model through the usual procedure.
Cluster-like coordinates in supersymmetric quantum field theory.
Neitzke, Andrew
2014-07-08
Recently it has become apparent that N = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.
Mean-field theory of echo state networks
NASA Astrophysics Data System (ADS)
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
The adhesion model as a field theory for cosmological clustering
Rigopoulos, Gerasimos
2015-01-01
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.
Comments on superstring field theory and its vacuum solution
NASA Astrophysics Data System (ADS)
Kroyter, Michael
2009-08-01
We prove that the NS cubic superstring field theories are classically equivalent, regardless of the choice of Y-2 in their definition, and illustrate it by an explicit evaluation of the action of Erler's solution. We then turn to examine this solution. First, we explain that its cohomology is trivial also in the Ramond sector. Then, we show that the boundary state corresponding to it is identically zero. We conclude that this solution is indeed a closed string vacuum solution despite the absence of a tachyon field on the BPS D-brane.
Liouville Field Theory and Log-Correlated Random Energy Models
NASA Astrophysics Data System (ADS)
Cao, Xiangyu; Rosso, Alberto; Santachiara, Raoul; Le Doussal, Pierre
2017-03-01
An exact mapping is established between the c ≥25 Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian free field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry-breaking methods. Operator product expansions in the LFT allow us to unveil novel universal behaviors of the log-correlated random energy class. High-precision numerical tests are given.
Liouville Field Theory and Log-Correlated Random Energy Models.
Cao, Xiangyu; Rosso, Alberto; Santachiara, Raoul; Le Doussal, Pierre
2017-03-03
An exact mapping is established between the c≥25 Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian free field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry-breaking methods. Operator product expansions in the LFT allow us to unveil novel universal behaviors of the log-correlated random energy class. High-precision numerical tests are given.
Field-dependent BRST transformations in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Lavrov, Peter M.; Lechtenfeld, Olaf
2013-10-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary Rξ gauges.
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
NASA Astrophysics Data System (ADS)
Román-Roy, Narciso
2009-11-01
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.
Vakonomic Constraints in Higher-Order Classical Field Theory
NASA Astrophysics Data System (ADS)
Campos, Cédric M.
2010-07-01
We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.
Testing chameleon theories with light propagating through a magnetic field
Brax, Philippe; Davis, Anne-Christine; Mota, David F.
2007-10-15
It was recently argued that the observed PVLAS anomaly can be explained by chameleon field theories in which large deviations from Newton's law can be avoided. Here we present the predictions for the dichroism and the birefringence induced in the vacuum by a magnetic field in these models. We show that chameleon particles behave very differently from standard axionlike particles (ALPs). We find that, unlike ALPs, the chameleon particles are confined within the experimental setup. As a consequence, the birefringence is always bigger than the dichroism in PVLAS-type experiments.
Causal field theory with an infinite speed of sound
NASA Astrophysics Data System (ADS)
Afshordi, Niayesh; Chung, Daniel J. H.; Geshnizjani, Ghazal
2007-04-01
We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.
Causal field theory with an infinite speed of sound
Afshordi, Niayesh; Chung, Daniel J. H.; Geshnizjani, Ghazal
2007-04-15
We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.
Regularization of identity based solution in string field theory
NASA Astrophysics Data System (ADS)
Zeze, Syoji
2010-10-01
We demonstrate that an Erler-Schnabl type solution in cubic string field theory can be naturally interpreted as a gauge invariant regularization of an identity based solution. We consider a solution which interpolates between an identity based solution and ordinary Erler-Schnabl one. Two gauge invariant quantities, the classical action and the closed string tadpole, are evaluated for finite value of the gauge parameter. It is explicitly checked that both of them are independent of the gauge parameter.
Motivating quantum field theory: the boosted particle in a box
NASA Astrophysics Data System (ADS)
Vutha, Amar C.
2013-07-01
It is a maxim often stated, yet rarely illustrated, that the combination of special relativity and quantum mechanics necessarily leads to quantum field theory. An elementary illustration is provided using the familiar particle in a box, boosted to relativistic speeds. It is shown that quantum fluctuations of momentum lead to energy fluctuations, which are inexplicable without a framework that endows the vacuum with dynamical degrees of freedom and allows particle creation/annihilation.
Generating functionals for Green's functions in gauge field theories
Bordag, M.; Kaschlun, L.; Matveev, V.A.; Robaschik, D.
1987-09-01
The structure of the generating functional of the one-particle-irreducible Green's functions in gauge field theories is investigated. Both axial as well as covariant gauge conditions are considered. For both cases, the general structure of the functionals is obtained, and a functional expansion with respect to nonlocal operators is given. The appearance of gauge-dependent operators in the case of the covariant gauge follows in a natural manner from the structure of the corresponding functional.
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.
Three-Body Nuclear Systems in Pionless Effective Field Theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared
2016-03-01
New perturbative techniques for three-body systems with contact interactions are discussed. Their application to pionless effective field theory (EF{Tnot π }) for nd scattering is shown, and their extension to bound states addressed. With the extension to bound states a leading-order EF{Tnot π } calculation of the triton charge radius and novel treatments of three-body forces are discussed.
Jost-Lehmann-Dyson representation in higher dimensional field theories
NASA Astrophysics Data System (ADS)
Maharana, Jnanadeva
2017-01-01
The Jost-Lehmann-Dyson representation is derived for massive scalar field theories in higher spacetime dimensions, D > 4, for the four point scattering amplitude. The representation is very crucial to investigate the analyticity properties of the amplitude. The axiomatic approach of Lehmann-Symanzik-Zimmermann is adopted to show the existence of such a representation. Consequently, a host of interesting results will follow from derivation of JLD representation such as proof of analyticity properties and asymptotic behavior of the amplitude.
Four-nucleon force in chiral effective field theory
Evgeny Epelbaum
2005-10-25
We derive the leading contribution to the four--nucleon force within the framework of chiral effective field theory. It is governed by the exchange of pions and the lowest--order nucleon--nucleon contact interaction and includes effects due to the nonlinear pion--nucleon couplings and the pion self interactions constrained by the chiral symmetry of QCD. The resulting 4NF does not contain any unknown parameters and can be tested in future few--and many--nucleon studies.
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.
Dynamical mean-field theory for flat-band ferromagnetism
NASA Astrophysics Data System (ADS)
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
From Archimedean L-Factors to Topological Field Theories
NASA Astrophysics Data System (ADS)
Gerasimov, Anton; Lebedev, Dimitri; Oblezin, Sergey
2011-06-01
We give a short account of our recent results on establishing a relation between topological field theories and Archimedean (∞-adic) geometry. First, we introduce a universal integral Baxter operator as a certain element of the spherical Hecke algebra {fancyscript{H}(G,K)}. Eigenvalues of the Baxter operator acting on spherical vectors in irreducible representations G are given by corresponding local Archimedean L-factors. We provide a quantum field theory interpretation of the local Archimedean L-factors as certain correlation functions in a two-dimensional type A equivariant topological linear sigma model on a disk D. Next, we introduce a q-version of the Archimedean L-factors and construct a particular representation of q-deformed Whittaker functions generalizing the Casselman-Shalika formula for p-adic class one Whittaker functions. This representation allows to formulate a q-version of Archimedean Langlands correspondence. Then, we construct a representation of q-version of the Archimedean L-factors as a certain correlation functions in three-dimensional equivariant linear sigma model on D × S 1. Finally, we propose an interpretation of the Archimedean Langlands correspondence as a mirror symmetry in the underlying topological quantum field theory.
Matching Contact Interactions in QED-NRQED Effective Field Theory
NASA Astrophysics Data System (ADS)
Dye, Steven; Gonderinger, Matthew; Paz, Gil
2017-01-01
In 2010 the proton charge radius was first extracted from muonic hydrogen and was found to have a value five standard deviations away from the regular hydrogen value. An effective field theory analysis using Non-Relativistic Quantum Electrodynamics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. One of the most promising avenues to resolve this puzzle is by muon-proton scattering. Such an experiment, called MUSE, is planned at the Paul Scherrer Institute in Switzerland. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still non-relativistic. The interaction between them can be described by a QED-NRQED effective field theory. Here we present elements of this effective field theory. In particular, we look at O (Zα) scattering up to power m2 /M2 , where m (M) is the muon (proton) mass, and O (Z2α2) scattering at leading power. We also take a brief look at O (Z2α2) at subleading power.
Consistent Kaluza-Klein truncations via exceptional field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Samtleben, Henning
2015-01-01
We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO( p, q) and CSO( p, q, r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides H p,q , thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D = 11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS5 × S 5), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.
Axionic field theory of (3+1)-dimensional Weyl semimetals
NASA Astrophysics Data System (ADS)
Goswami, Pallab; Tewari, Sumanta
2013-12-01
From a direct calculation of the anomalous Hall conductivity and an effective electromagnetic action obtained via Fujikawa's chiral rotation technique, we conclude that an axionic field theory with a nonquantized coefficient describes the electromagnetic response of the (3+1)-dimensional Weyl semimetal. The coefficient is proportional to the momentum space separation of the Weyl nodes. Akin to the Chern-Simons field theory of quantum Hall effect, the axion field theory violates gauge invariance in the presence of the boundary, which is cured by the chiral anomaly of the surface states via the Callan-Harvey mechanism. This provides a unique solution for the radiatively induced CPT-odd term in the electromagnetic polarization tensor of the Lorentz violating spinor electrodynamics, where the source of the Lorentz violation is a constant axial 4-vector term for the Dirac fermion. A direct linear response calculation also establishes anomalous thermal Hall effect and a Wiedemann-Franz law, but thermal Hall conductivity does not directly follow from the well known formula for the gravitational chiral anomaly.
Hamiltonian truncation approach to quenches in the Ising field theory
NASA Astrophysics Data System (ADS)
Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.
2016-10-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
Constraints on RG flow for four dimensional quantum field theories
NASA Astrophysics Data System (ADS)
Jack, I.; Osborn, H.
2014-06-01
The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve a, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric G on the space of couplings and give rise to gradient flow like equations for a, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings e2σ to a form which involves running couplings gσ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa β-functions for a general scalar/fermion theory are obtained and the three loop contribution to the metric G for this theory is also calculated. These results are used to check the gradient flow equations to higher order than previously. It is shown that these are only valid when β→B, a modified β-function, and that the equations provide strong constraints on the detailed form of the three loop Yukawa β-function. N=1 supersymmetric Wess-Zumino theories are also considered as a special case. It is shown that the metric for the complex couplings in such theories may be restricted to a hermitian form.
The ontology of quantum field theory: Structural realism vindicated?
Glick, David
2016-10-01
In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed theories in science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Grassmann phase space methods for fermions. II. Field theory
NASA Astrophysics Data System (ADS)
Dalton, B. J.; Jeffers, J.; Barnett, S. M.
2017-02-01
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker-Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
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.
Fowler Nordheim theory of carbon nanotube based field emitters
NASA Astrophysics Data System (ADS)
Parveen, Shama; Kumar, Avshish; Husain, Samina; Husain, Mushahid
2017-01-01
Field emission (FE) phenomena are generally explained in the frame-work of Fowler Nordheim (FN) theory which was given for flat metal surfaces. In this work, an effort has been made to present the field emission mechanism in carbon nanotubes (CNTs) which have tip type geometry at nanoscale. High aspect ratio of CNTs leads to large field enhancement factor and lower operating voltages because the electric field strength in the vicinity of the nanotubes tip can be enhanced by thousand times. The work function of nanostructure by using FN plot has been calculated with reverse engineering. With the help of modified FN equation, an important formula for effective emitting area (active area for emission of electrons) has been derived and employed to calculate the active emitting area for CNT field emitters. Therefore, it is of great interest to present a state of art study on the complete solution of FN equation for CNTs based field emitter displays. This manuscript will also provide a better understanding of calculation of different FE parameters of CNTs field emitters using FN equation.
R&D for the Post-EP Processes of Superconducting RF Cavity
Saeki, Takayuki; Funahashi, Y.; Hayano, H.; Kato, Seigo; Nishiwaki, Michiru; Sawabe, Motoaki; Ueno, Kenji; Watanabe, K.; Antoine, Claire; Berry, Stefurn; Eozenou, F.; Gasser, Y.; Visentin, B.; Clemens, William A.; Geng, Rongli; Manus, Robert; Tyagi, Puneet
2009-11-01
The Electro-Polishing (EP) process is the best candidate of final surface treatment for the production of ILC cavities. Nevertheless, the broad distribution of the gradient caused by field emitters in cavities is sitll a serious problem for the EP process. A candidate source of field emitter is the sulfur component which is produced in the EP process and remains the inner-surface of cavities. We studied the effect of Ethanole- and degreaser-rinse processes after the EP process by a unique method. Moreover, we tried to test the sponge cleaning as the post-EP process to remove the field emitter inside the cavcity. This article describe the results of series tests of the post-EP process at KEK.
Prequantum classical statistical field theory: background field as a source of everything?
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2011-07-01
Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's "double solution" approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special "prequantum fields": the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the "photonic field" (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of "vacuum fluctuations") might play the role of a source of such pulses, i.e., the source of everything.
Translational symmetry breaking in field theories and the cosmological constant
NASA Astrophysics Data System (ADS)
Evans, Nick; Morris, Tim R.; Scott, Marc
2016-01-01
We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as q ¯q and q ¯F(2 n )q . Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in R2 gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.
Unifying Self-Consistent Field Theory for Weak Polyelectrolytes
NASA Astrophysics Data System (ADS)
Witte, Kevin; Won, You-Yeon
2008-03-01
A self-consistent field (SCF) theory for weak polyelectrolytes has been derived from a grand canonical partition function. The formalism accounts for the location and mixing of the charged and uncharged polymer species, treating the local (spatially dependent) charge fraction as a field variable with which to minimize the total free energy. This method of the derivation gives the resulting equations, especially those governing the local charge fraction, that are identical to the results obtained by Szleifer and coworkers (J. Polym. Sci. B Polym. Phys., 2006) who built upon the mean-field ``annealed'' free energy expression proposed by Raphael and Joanny (Europhys. Lett., 1990). However, we show that these results are further identical to the ``two-state'' model of Borukhov, Andelman and Orland (Eur. Phys. J. B, 1998), namely, the potential field due to the polymer charges with which the chains interact and the local charge fraction are shown to be exactly equal. This annealed model is derived by averaging the partition function with regard to the monomer charges. The charged and uncharged states are weighted by their probabilities which is, in our notation, the bulk charge fraction and one minus the bulk charge fraction, respectively. The utility of this theory is demonstrated by comparing its predictions against various experimental results from bulk potentiometric measurements and also from polyelectrolyte brush compression studies.
Relative entanglement entropies in 1 + 1-dimensional conformal field theories
NASA Astrophysics Data System (ADS)
Ruggiero, Paola; Calabrese, Pasquale
2017-02-01
We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S( ρ 1∥ ρ 0) between two given reduced density matrices ρ 1 and ρ 0 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr( ρ 1 ρ 0 n - 1 ) and define a set of Rényi relative entropies S n ( ρ 1∥ ρ 0). We compute these quantities for integer values of the parameter n and derive via the replica limit the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i∂ ϕ, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement.
Quantum Field Theory of Kosterlitz-Thouless Phase Transitions.
NASA Astrophysics Data System (ADS)
Ogilvie, Michael Charles
1980-12-01
A general quantum field-theoretic formalism for the study of Kosterlitz-Thouless phase transition is developed and applied to several models. The structure of the free, massless scalar field is discussed, making explicit its connection with the Gaussian model. The close connection of the spin-wave and vortex operators with two-dimensional fermion-boson equivalences is stressed. The critical behavior of the planar model is reviewed, using field-theoretic methods applied to the sine-Gordon model. The Kosterlitz -Thouless phase transition in two-dimensional dislocation -mediated melting is studied using a vector generalization of the sine-Gordon model. Recent second-order renormalization group calculations are confirmed, and the issue of universal third-order corrections is discussed. It is shown that the Gross-Neveu model can be interpreted as a massive theory associated with a Kosterlitz-Thouless critical point. Finally, the Ising and Baxter models are studied using the methods developed here. It is shown that the vortex and spin-wave excitations in the Ising model conspire to produce a free, massive Majorana fermion field theory in the continuum limit. The formalism is then extended to the Baxter model. Recent results on the Baxter and Ashkin-Teller models are rederived and extended.
C*-algebraic scattering theory and explicitly solvable quantum field theories
NASA Astrophysics Data System (ADS)
Warchall, Henry A.
1985-06-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.
NASA Astrophysics Data System (ADS)
Gan, W. S.
2008-12-01
This paper is to be dedicated to Prof C N Yang's 85th birthday celebration because the idea here was inspired by Prof Yang's public lecture in Singapore in 2006. There are many similarities between electromagnetic waves and acoustic waves. Maxwell's equations for em waves is the oldest gauge theory. We discover symmetries in the pair of wave equations in the acoustic stress field and the velocity field. We also derive a new equation in terms of the stress field for sound propagation in solids. This is different from the Christoffel's equation which is in term of the velocity field. We feel that stress field can better characterize the elastic properties of the sound waves. We also derive the acoustic gauge field condition and gauge invariance and symmetries for the acoustic fields. We also apply symmetries to study negative refraction. Note from Publisher: This article contains the abstract only.
Comments on complete actions for open superstring field theory
NASA Astrophysics Data System (ADS)
Matsunaga, Hiroaki
2016-11-01
We clarify a Wess-Zumino-Witten-like structure including Ramond fields and propose one systematic way to construct gauge invariant actions: Wess-Zumino-Witten-like complete action S WZW. We show that Kunitomo-Okawa's action proposed in arXiv:1508.00366 can obtain a topological parameter dependence of Ramond fields and belongs to our WZW-like framework. In this framework, once a WZW-like functional {{A}}_{η }={{A}}_{η}[Ψ ] of a dynamical string field Ψ is constructed, we obtain one realization of S WZW[Ψ] parametrized by Ψ. On the basis of this way, we construct an action tilde{S} whose on-shell condition is equivalent to the Ramond equations of motion proposed in arXiv:1506.05774. Using these results, we provide the equivalence of two theories: arXiv:1508.00366 and arXiv:1506.05774.
Quantum field theory in non-integer dimensions
Eyink, G.L.
1987-01-01
In a 1973 paper entitled Quantum Field-Theory Models in Less Than 4 Dimensions, Kenneth G. Wilson studied field-theories for spacetime dimension d between 2 and 4. With unconventional renormalizations, these models were found to have non-Gaussian ultraviolet renormalization group fixed points. Wilson's method was perturbative dimensional regularization: the Feynman-graph integrals were analytically continued to non-integer d. His work left open the question of the nonperturbative existence of the models. Since that landmark paper, Yuval Gefen, Amnon Aharony and Benoit B. Mandelbrot have shown that Ising spin models on fractal lattices have critical properties like those predicted for non-integer dimensions by the analytic continuation, or {epsilon}-expansion method. This work shows that fractal lattices and continua provide also a nonperturbative definition of field-theories in non-integer dimensions. The fractal point-sets employed are the Sierpinski carpets and their higher-dimensional generalizations. This class of point-sets has a tunable dimension which allows the approach to four from below. Furthermore, the carpets have discrete groups of scale or dilation invariances and infinite order of ramification. A class of scalar field models are defined on these sets which should reduce to the standard models when d {nearrow}4. The propagator for these models is given by a proper-time or heat-kernel representation. For this propagator, reflection-positivity is established, a general scaling law is conjectured (and established in a special case), and the perturbative renormalizability shown to be governed by the spectral dimensionality. Scalar models with another choice of propagator, the hierarchical propagator, are studied by rigorous renormalization-group methods.
Quantum Field Theory Tools:. a Mechanism of Mass Generation of Gauge Fields
NASA Astrophysics Data System (ADS)
Flores-Baez, F. V.; Godina-Nava, J. J.; Ordaz-Hernandez, G.
We present a simple mechanism for mass generation of gauge fields for the Yang-Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang-Mills theories without Higgs bosons.
Quantum field theory on toroidal topology: Algebraic structure and applications
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
2014-05-01
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RD-d is developed from a Lie-group representation and c*c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real- and imaginary-time versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on
Primordial magnetic field and kinetic theory with Berry curvature
NASA Astrophysics Data System (ADS)
Bhatt, Jitesh R.; Pandey, Arun Kumar
2016-08-01
We study the generation of a magnetic field in primordial plasma of standard model particles at a temperature T >80 TeV —much higher than the electroweak scale. It is assumed that there is an excess number of right-handed electrons compared to left-handed positrons in the plasma. Using the Berry-curvature modified kinetic theory to incorporate the effect of the Abelian anomaly, we show that this chiral imbalance leads to the generation of a hypermagnetic field in the plasma in both the collision dominated and collisionless regimes. It is shown that, in the collision dominated regime, the chiral-vorticity effect can generate finite vorticity in the plasma together with the magnetic field. Typical strength of the generated magnetic field is 1 027 G at T ˜80 TeV with the length scale 1 05/T , whereas the Hubble length scale is 1 013/T . Furthermore, the instability can also generate a magnetic field of the order 1 031 G at a typical length scale 10 /T . But there may not be any vorticity generation in this regime. We show that the estimated values of the magnetic field are consistent with the bounds obtained from current observations.
Modified f( R, T) gravity theory and scalar field cosmology
NASA Astrophysics Data System (ADS)
Singh, Vijay; Singh, C. P.
2015-03-01
In this paper, we explore the behaviors of scalar field in modified f( R, T) gravity theory within the framework of a flat Friedmann-Robertson-Walker cosmological model. The universe is assumed to be filled with two non-interacting matter sources, scalar field (normal or phantom) with scalar potential and matter contribution due to f( R, T) action. We first explore a model where the potential is a constant, and the universe evolves as a de Sitter type. This model is compatible with phantom scalar field only which gives fine tuning with the recent observations. The model exhibits a wide variety of early time physical phenomena that eventually behaves like a cosmological constant at late times. The model shows transition from decelerated to accelerated expansion of the universe. We also explore a model where the scalar field potential and the scale factor evolve exponentially as a scalar field. This model is compatible with normal scalar field only and describes transition from inflationary to the decelerated phase at early times and quintessence to phantom phase at late times. We constraint our results with the recent observational data and find that some values of parameters are consistent with SNe Ia and H( z)+SNe Ia data to describe accelerated expansion only whereas some one give decelerated and accelerated expansions with H( z), WMAP7 and WMAP7+BAO+ H( z) observational data.
The effective field theory of cosmological large scale structures
Carrasco, John Joseph M.; Hertzberg, Mark P.; Senatore, Leonardo
2012-09-20
Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is c^{2}_{s} ≈ 10^{–6}c^{2} and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)^{4}. As a result, the predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k ≃ 0.24h Mpc^{–1}.
Topics in topological and holomorphic quantum field theory
NASA Astrophysics Data System (ADS)
Vyas, Ketan
We investigate topological quantum field theories (TQFTs) in two, three, and four dimensions, as well as holomorphic quantum field theories (HQFTs) in four dimensions. After a brief overview of the two-dimensional (gauged) A and B models and the corresponding the category of branes, we construct analogous three-dimensional (gauged) A and B models and discuss the two-category of boundary conditions. Compactification allows us to identify the category of line operators in the three-dimensional A and B models with the category of branes in the corresponding two-dimensional A and B models. Furthermore, we use compactification to identify the two-category of surface operators in the four-dimensional GL theory at t = 1 and t = i with the two-category of boundary conditions in the corresponding three-dimensional A and B model, respectively. We construct a four-dimensional HQFT related to N = 1 supersymmetric quantum chromodynamics (SQCD) with gauge group SU(2) and two flavors, as well as a four-dimensional HQFT related to the Seiberg dual chiral model. On closed K ̈ahler surfaces with h^(2,0) > 0, we show that the correlation functions of holomorphic SQCD formally compute certain Donaldson invariants. For simply-connected elliptic surfaces (and their blow-ups), we show that the corresponding correlation functions in the holomorphic chiral model explicitly compute these Donaldson invariants.
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.
Effective Field Theory approach to heavy quark fragmentation
NASA Astrophysics Data System (ADS)
Fickinger, Michael; Fleming, Sean; Kim, Chul; Mereghetti, Emanuele
2016-11-01
Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the b-quark fragmentation function from electron-positron annihilation data at the Z-boson peak at next-to-next-to leading order with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the b-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Using an approach based on effective field theory allows us to systematically control theoretical errors. While the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the b-quark fragmentation function at smaller values of momentum fraction.
Effective field theory approach to heavy quark fragmentation
Fickinger, Michael; Fleming, Sean; Kim, Chul; ...
2016-11-17
Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the b-quark fragmentation function from electron-positron annihilation data at the Z-boson peak at next-to-next-to leading order with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the b-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Usingmore » an approach based on effective field theory allows us to systematically control theoretical errors. Furthermore, while the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the b-quark fragmentation function at smaller values of momentum fraction.« less
Effective field theory approach to heavy quark fragmentation
Fickinger, Michael; Fleming, Sean; Kim, Chul; Mereghetti, Emanuele
2016-11-17
Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the b-quark fragmentation function from electron-positron annihilation data at the Z-boson peak at next-to-next-to leading order with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the b-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Using an approach based on effective field theory allows us to systematically control theoretical errors. Furthermore, while the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the b-quark fragmentation function at smaller values of momentum fraction.
Is the effective field theory of dark energy effective?
NASA Astrophysics Data System (ADS)
Linder, Eric V.; Sengör, Gizem; Watson, Scott
2016-05-01
The effective field theory of cosmic acceleration systematizes possible contributions to the action, accounting for both dark energy and modifications of gravity. Rather than making model dependent assumptions, it includes all terms, subject to the required symmetries, with four (seven) functions of time for the coefficients. These correspond respectively to the Horndeski and general beyond Horndeski class of theories. We address the question of whether this general systematization is actually effective, i.e. useful in revealing the nature of cosmic acceleration when compared with cosmological data. The answer is no and yes: there is no simple time dependence of the free functions—assumed forms in the literature are poor fits, but one can derive some general characteristics in early and late time limits. For example, we prove that the gravitational slip must restore to general relativity in the de Sitter limit of Horndeski theories, and why it doesn't more generally. We also clarify the relation between the tensor and scalar sectors, and its important relation to observations; in a real sense the expansion history H(z) or dark energy equation of state w(z) is 1/5 or less of the functional information! In addition we discuss the de Sitter, Horndeski, and decoupling limits of the theory utilizing Goldstone techniques.
Synchrotron radiation in strongly coupled conformal field theories
Athanasiou, Christiana; Chesler, Paul M.; Liu, Hong; Rajagopal, Krishna; Nickel, Dominik
2010-06-15
Using gauge/gravity duality, we compute the energy density and angular distribution of the power radiated by a quark undergoing circular motion in strongly coupled N=4 supersymmetric Yang-Mills theory. We compare the strong coupling results to those at weak coupling, finding them to be very similar. In both regimes, the angular distribution of the radiated power is in fact similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle {alpha}{approx}1/{gamma}. To an observer far away from the quark, the emitted radiation appears as a short periodic burst, just like the light from a lighthouse does to a ship at sea. Our strong coupling results are valid for any strongly coupled conformal field theory with a dual classical gravity description.
Nonstandard connections in k-cosympletic field theory
NASA Astrophysics Data System (ADS)
Muñoz-Lecanda, Miguel-C.; Salgado, Modesto; Vilariño, Silvia
2005-12-01
In the jet-bundle description of time-dependent mechanics there are some elements, such as the Lagrangian energy and the construction of the Hamiltonian formalism, which require the prior choice of a connection. This situation is analyzed by Echeverría-Enríquez et al. [J. Phys. A 28, 5553-5567 (1995)]. The aim of this paper is to extend the results in that paper to first order field theory, using the k-cosymplectic formalism described by de León and co-workers [J. Math. Phys. 39, 876-893 (1998); 42, 2092-2104 (2001)]. If the trivial configuration bundle of a Lagrangian system is endowed with one connection, different from the trivial one given by the product structure, we study the consequences on the geometric elements of the theory, the dynamical equations and the variational principles.
Generally covariant vs. gauge structure for conformal field theories
Campigotto, M.; Fatibene, L.
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
Scaling Deviations for Neutrino Reactions in Aysmptotically Free Field Theories
DOE R&D Accomplishments Database
Wilczek, F. A.; Zee, A.; Treiman, S. B.
1974-11-01
Several aspects of deep inelastic neutrino scattering are discussed in the framework of asymptotically free field theories. We first consider the growth behavior of the total cross sections at large energies. Because of the deviations from strict scaling which are characteristic of such theories the growth need not be linear. However, upper and lower bounds are established which rather closely bracket a linear growth. We next consider in more detail the expected pattern of scaling deviation for the structure functions and, correspondingly, for the differential cross sections. The analysis here is based on certain speculative assumptions. The focus is on qualitative effects of scaling breakdown as they may show up in the X and y distributions. The last section of the paper deals with deviations from the Callan-Gross relation.
Parton physics from large-momentum effective field theory
NASA Astrophysics Data System (ADS)
Ji, XiangDong
2014-07-01
Parton physics, when formulated as light-front correlations, are difficult to study non-perturbatively, despite the promise of light-front quantization. Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture of a hadron moving at asymptotically large momentum. Here I formulate the approach in the language of an effective field theory for a large hadron momentum P in lattice QCD, LaMET for short. I show that using this new effective theory, parton properties, including light-front parton wave functions, can be extracted from lattice observables in a systematic expansion of 1/ P, much like that the parton distributions can be extracted from the hard scattering data at momentum scales of a few GeV.
An effective field theory for coupled-channel scattering
NASA Astrophysics Data System (ADS)
Cohen, Thomas D.; Gelman, Boris A.; van Kolck, U.
2004-05-01
The problem of describing low-energy two-body scattering for systems with two open channels with different thresholds is addressed in the context of an effective field theory. In particular, the problem where the threshold is unnaturally small and the cross section at low energy is unnaturally large is considered. It is shown that the lowest-order point coupling associated with the mixing of the channels scales as Λ-2 rather than Λ-1 (the scaling of the same-channel coupling and the scaling in a single-channel case) where Λ is the ultraviolet cutoff. The renormalization of the theory at lowest order is given explicitly. The treatment of higher orders is straightforward. The potential implications for systems with deep open channels are discussed.
Action and entanglement in gravity and field theory.
Neiman, Yasha
2013-12-27
In nongravitational quantum field theory, the entanglement entropy across a surface depends on the short-distance regularization. Quantum gravity should not require such regularization, and it has been conjectured that the entanglement entropy there is always given by the black hole entropy formula evaluated on the entangling surface. We show that these statements have precise classical counterparts at the level of the action. Specifically, we point out that the action can have a nonadditive imaginary part. In gravity, the latter is fixed by the black hole entropy formula, while in nongravitating theories it is arbitrary. From these classical facts, the entanglement entropy conjecture follows by heuristically applying the relation between actions and wave functions.
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.
Energy flux positivity and unitarity in conformal field theories.
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-07
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux.
Effective field theory for few-boson systems
NASA Astrophysics Data System (ADS)
Bazak, Betzalel; Eliyahu, Moti; van Kolck, Ubirajara
2016-11-01
We study universal bosonic few-body systems within the framework of effective field theory at leading order (LO). We calculate binding energies of systems of up to six particles and the atom-dimer scattering length. Convergence to the limit of zero-range two- and three-body interactions is shown, indicating that no additional few-body interactions need to be introduced at LO. Generalizations of the Tjon line are constructed, showing correlations between few-body binding energies and the binding energy of the trimer, for a given dimer energy. As a specific example, we implement our theory for 4He atomic systems and show that the results are in surprisingly good agreement with those of sophisticated 4He-4He potentials. Potential implications for the convergence of the EFT expansion are discussed.
Membrane stress profiles from self-consistent field theory
NASA Astrophysics Data System (ADS)
Ting, Christina L.; Müller, Marcus
2017-03-01
Using self-consistent field theory (SCFT), we develop an accurate, local expression for the stress profiles in membranes and soft matter interfaces, in general. The bond stresses are expressed in terms of pre-computed chain propagators, which are used to describe the statistical weight of the molecules and therefore require minimal additional calculations. In addition, we overcome the resolution limit of the molecular bond length by including the Irving and Kirkwood bond assignment and recover a constant normal stress profile across an interface. Using this theory, we find that the membrane lateral stress profile contains repulsive (positive) stresses in the regions of the head and tail groups, and attractive (negative) stresses near the hydrophobic/hydrophilic interface. We also verify that the zeroth and first moments of the stress profile correspond to the thermodynamic tension and product of the bending modulus and the spontaneous curvature, respectively.
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.
Energy Flux Positivity and Unitarity in Conformal Field Theories
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-07
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop light like poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux.
Open effective field theories from deeply inelastic reactions
NASA Astrophysics Data System (ADS)
Braaten, Eric; Hammer, H.-W.; Lepage, G. Peter
2016-09-01
Effective field theories have often been applied to systems with deeply inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have been taken into account in previous work by adding local anti-Hermitian terms to the effective Hamiltonian. Here, we show that when multiparticle systems are considered, an additional modification is required in equations governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum particles and show that it satisfies a Lindblad equation, with local Lindblad operators determined by the anti-Hermitian terms in the effective Hamiltonian density.
Open Effective Field Theories from Deeply Inelastic Reactions
NASA Astrophysics Data System (ADS)
Braaten, Eric; Hammer, Hans-Werner; Lepage, G. Peter
2017-01-01
Effective field theories have often been applied to systems with inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have been taken into account in previous work by adding local anti-Hermitian terms to the effective Hamiltonian density. We show that an additional modification is required in equations governing the density matrix when multi-particle states are considered. We define an effective density matrix by tracing out states containing high-momentum particles, and show that it satisfies a Lindblad equation, with Lindblad operators determined by the anti-Hermitian terms in the effective Hamiltonian density. This research was supported in part by the Department of Energy, the National Science Foundation, and the Simons Foundation.
Energy Flux Positivity and Unitarity in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-01
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux.
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.
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Mean field theory for U(n) dynamical groups
NASA Astrophysics Data System (ADS)
Rosensteel, G.
2011-04-01
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
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.
Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time
NASA Astrophysics Data System (ADS)
Benisty, David; Guendelman, E. I.
2016-09-01
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.
Morton, J Bruce
2014-06-01
Buss and Spencer's monograph is an impressive achievement that is sure to have a lasting impact on the field of child development. The dynamic field theory (DFT) model that forms the heart of this contribution is ambitious in scope, detailed in its implementation, and rigorously tested against data, old and new. As such, the ideas contained in this fine document represent a qualitative advance in our understanding of young children's behavior, and lay a foundation for future research into the developmental origins of executive functioning.
Forms of null Lagrangians in field theories of continuum mechanics
NASA Astrophysics Data System (ADS)
Kovalev, V. A.; Radaev, Yu. N.
2012-02-01
The divergence representation of a null Lagrangian that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null Lagrangian can contain up to 15 independent elements in total. The general form of a null Lagrangian in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null Lagrangian for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null Lagrangians are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to formulate a divergence conservation law on solutions to the system.
Primordial statistical anisotropies: the effective field theory approach
Abolhasani, Ali Akbar; Akhshik, Mohammad; Emami, Razieh; Firouzjahi, Hassan E-mail: m.akhshik@ipm.ir E-mail: firouz@ipm.ir
2016-03-01
In this work we present the effective field theory of primordial statistical anisotropies generated during anisotropic inflation involving a background U(1) gauge field. Besides the usual Goldstone boson associated with the breaking of time diffeomorphism we have two additional Goldstone bosons associated with the breaking of spatial diffeomorphisms. We further identify these two new Goldstone bosons with the expected two transverse degrees of the U(1) gauge field fluctuations. Upon defining the appropriate unitary gauge, we present the most general quadratic action which respects the remnant symmetry in the unitary gauge. The interactions between various Goldstone bosons leads to statistical anisotropy in curvature perturbation power spectrum. Calculating the general results for power spectrum anisotropy, we recover the previously known results in specific models of anisotropic inflation. In addition, we present novel results for statistical anisotropy in models with non-trivial sound speed for inflaton fluctuations. Also we identify the interaction which leads to birefringence-like effects in anisotropic power spectrum in which the speed of gauge field fluctuations depends on the direction of the mode propagation and the two polarization of gauge field fluctuations contribute differently in statistical anisotropy. As another interesting application, our EFT approach naturally captures interactions generating parity violating statistical anisotropies.
A Chern-Simons effective field theory for the Pfaffian quantum Hall state
NASA Astrophysics Data System (ADS)
Fradkin, Eduardo; Nayak, Chetan; Tsvelik, Alexei; Wilczek, Frank
1998-04-01
We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2) 2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
LETTER TO THE EDITOR: Quantum field theory and phylogenetic branching
NASA Astrophysics Data System (ADS)
Jarvis, P. D.; Bashford, J. D.
2001-12-01
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching events. The spatial dimension L is the number of leaves of the evolutionary tree under consideration. Momentum conservation modulo ←1 scattering corresponds to tree edge labelling using binary L-vectors. The bilocal quadratic term allows for momentum-dependent rate constants - only the tree or trees compatible with selected nonzero edge rates contribute to the branching probability distribution. Applications to models of evolutionary branching processes are discussed.
Three-body systems in pionless effective field theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared
2016-04-01
Investigations of three-body nuclear systems using pionless effective field theory (EFTπ̸) are reviewed. The history of EFTπ̸ in nd and pd scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in pd scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in nd scattering are also considered and the utility of EFTπ̸ for addressing them.
Applications of random field theory to functional connectivity.
Worsley, K J; Cao, J; Paus, T; Petrides, M; Evans, A C
1998-01-01
Functional connectivity between two voxels or regions of voxels can be measured by the correlation between voxel measurements from either PET CBF or BOLD fMRI images in 3D. We propose to look at the entire 6D matrix of correlations between all voxels and search for 6D local maxima. The main result is a new theoretical formula based on random field theory for the p-value of these local maxima, which distinguishes true correlations from background noise. This can be applied to crosscorrelations between two different sets of images--such as activations under two different tasks, as well as autocorrelations within the same set of images.
Collective field theory of a singular supersymmetric matrix model
de Mello Koch, R.; Rodrigues, J.P.
1995-05-15
The supersymmetric collective field theory with the potential {ital v}{prime}({ital x})={omega}{ital x}{minus}{eta}/{ital x} is studied. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeroes of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a Majorana fermion. The {ital x} space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
Atomistic force field for alumina fit to density functional theory
Sarsam, Joanne; Finnis, Michael W.; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al{sub 2}O{sub 3}), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
Mean field theory studies of surface reactions on disordered substrates
NASA Astrophysics Data System (ADS)
Cortés, Joaquín.; Narváez, Ana; Puschmann, Heinrich; Valencia, Eliana
2003-03-01
A mean field theory (MFT) in the site and pair approximations of a surface reaction system on a disordered substrate showing geometric heterogeneity is proposed, characterizing the substrate completely through the set { qi} of probabilities that a surface site has i neighbours that belong to the substrate in the model. The MFT results allow the interpretation of the Monte Carlo (MC) simulations carried out for the ZGB algorithm at instantaneous and finite rates over a series heterogeneous substrates corresponding to percolation clusters. The change in the character of the irreversible phase transitions (IPT) with the degree of disorder or branching of the substrate and its theoretical interpretation are analyzed.
Quark-gluon plasma and topological quantum field theory
NASA Astrophysics Data System (ADS)
Luo, M. J.
2017-03-01
Based on an analogy with topologically ordered new state of matter in condensed matter systems, we propose a low energy effective field theory for a parity conserving liquid-like quark-gluon plasma (QGP) around critical temperature in quantum chromodynamics (QCD) system. It shows that below a QCD gap which is expected several times of the critical temperature, the QGP behaves like topological fluid. Many exotic phenomena of QGP near the critical temperature discovered at Relativistic Heavy Ion Collision (RHIC) are more readily understood by the suggestion that QGP is a topologically ordered state.
Bayesian analysis of truncation errors in chiral effective field theory
NASA Astrophysics Data System (ADS)
Melendez, J.; Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2016-09-01
In the Bayesian approach to effective field theory (EFT) expansions, truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. By encoding expectations about the naturalness of EFT expansion coefficients for observables, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. We extend and test previous calculations of DOB intervals for chiral EFT observables, examine correlations between contributions at different orders and energies, and explore methods to validate the statistical consistency of the EFT expansion parameter. Supported in part by the NSF and the DOE.
Nuclear structure and reactions using lattice effective field theory
NASA Astrophysics Data System (ADS)
Rupak, Gautam
2016-09-01
Effective field theory (EFT) formulated on a space-time lattice provides a model-independent framework for ab initio nuclear structure and reaction calculations. The EFT interactions are rooted in quantum chromodynamics through low energy symmetry constraints. In this talk I present several recent developments in lattice EFT, in particular I present the so called adiabatic projection method that enables elastic and in-elastic reaction calculations. Bound state properties of atomic nuclei such as carbon and oxygen will also be presented. Partial support from US National Science Foundation Grant PHY-1307453 is acknowledged.
Wilsonian matching of effective field theory with underlying QCD
Harada, Masayasu; Yamawaki, Koichi
2001-07-01
We propose a novel way of matching effective field theory with the underlying QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive Wilsonian matching conditions between current correlators obtained by the operator product expansion in QCD and those by the hidden local symmetry (HLS) model. This determines without much ambiguity the bare parameters of the HLS at the cutoff scale in terms of the QCD parameters. Physical quantities for the {pi} and {rho} system are calculated by the Wilsonian RGE{close_quote}s from the bare parameters in remarkable agreement with the experiment.
Black hole thermodynamics, stringy dualities and double field theory
NASA Astrophysics Data System (ADS)
Arvanitakis, Alex S.; Blair, Chris D. A.
2017-03-01
We discuss black hole thermodynamics in the manifestly duality invariant formalism of double field theory (DFT). We reformulate and prove the first law of black hole thermodynamics in DFT, using the covariant phase space approach. After splitting the full O(D, D) invariant DFT into a Kaluza–Klein-inspired form where only n coordinates are doubled, our results provide explicit duality invariant mass and entropy formulas. We illustrate how this works by discussing the black string solution and its T-duals.
Quantum field theory results for neutrino oscillations and new physics
Delepine, D.; Gonzalez Macias, Vannia; Khalil, Shaaban; Lopez Castro, G.
2009-05-01
The CP asymmetry in neutrino oscillations, assuming new physics at production and/or detection processes, is analyzed. We compute this CP asymmetry using the standard quantum field theory within a general new physics scenario that may generate new sources of CP and flavor violation. Well-known results for the CP asymmetry are reproduced in the case of V-A operators, and additional contributions from new physics operators are derived. We apply this formalism to SUSY extensions of the standard model where the contributions from new operators could produce a CP asymmetry observable in the next generation of neutrino experiments.
Effective field theory of dark matter from membrane inflationary paradigm
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan; Dasgupta, Arnab
2016-09-01
In this article, we have studied the cosmological and particle physics constraints on dark matter relic abundance from effective field theory of inflation from tensor-to-scalar ratio (r), in case of Randall-Sundrum single membrane (RSII) paradigm. Using semi-analytical approach we establish a direct connection between the dark matter relic abundance (ΩDMh2) and primordial gravity waves (r), which establishes a precise connection between inflation and generation of dark matter within the framework of effective field theory in RSII membrane. Further assuming the UV completeness of the effective field theory perfectly holds good in the prescribed framework, we have explicitly shown that the membrane tension, σ ≤ O(10-9) Mp4, bulk mass scale M5 ≤ O(0.04 - 0.05) Mp, and cosmological constant Λ˜5 ≥ - O(10-15) Mp5, in RSII membrane plays the most significant role to establish the connection between dark matter and inflation, using which we have studied the features of various mediator mass scale suppressed effective field theory "relevant operators" induced from the localized s, t and u channel interactions in RSII membrane. Taking a completely model independent approach, we have studied an exhaustive list of tree-level Feynman diagrams for dark matter annihilation within the prescribed setup and to check the consistency of the obtained results, further we apply the constraints as obtained from recently observed Planck 2015 data and Planck + BICEP2 + Keck Array joint data sets. Using all of these derived results we have shown that to satisfy the bound on, ΩDMh2 = 0.1199 ± 0.0027, as from Planck 2015 data, it is possible to put further stringent constraint on r within, 0.01 ≤ r ≤ 0.12, for thermally averaged annihilation cross-section of dark matter, < σv > ≈ O(10-28 - 10-27) cm3 / s, which are very useful to constrain various membrane inflationary models.
Derivation of anomalous hydrodynamics from quantum field theory
NASA Astrophysics Data System (ADS)
Hongo, Masaru; Hayata, Tomoya; Hidaka, Yoshimasa; Minami, Yuki; Noumi, Toshifumi
2014-09-01
Hydrodynamics is a low-energy effective theory which describes a long-distance and long-time behavior of many-body systems. It has been recently pointed out that triangle anomalies affect macroscopic transport properties and generate anomaly-induced transports. These transport phenomena have a common feature that they are dissipationless, or in other words, they don't cause the entropy production. One example is the chiral magnetic effect, which represents the existence of a dissipationless vector current along the magnetic field and is expected to occur in ultra-relativistic heavy ion collisions. In this study, we derive anomalous hydrodynamic equations from the point of view of quantum field theory. Assuming the local Gibbs distribution at initial time, we derive a thermodynamic potential for relativistic hydrodynamics. This action has a form in the curved space-time whose metric is determined by the thermodynamic variables such as the temperature. We show that anomaly-induced transports manifest from this thermodynamic potential if systems do not have the parity symmetry, and, therefore, are dissipationless. We also discuss a relation between our work and other recent approaches that aim at deriving hydrodynamic equations for the parity-violating systems. Hydrodynamics is a low-energy effective theory which describes a long-distance and long-time behavior of many-body systems. It has been recently pointed out that triangle anomalies affect macroscopic transport properties and generate anomaly-induced transports. These transport phenomena have a common feature that they are dissipationless, or in other words, they don't cause the entropy production. One example is the chiral magnetic effect, which represents the existence of a dissipationless vector current along the magnetic field and is expected to occur in ultra-relativistic heavy ion collisions. In this study, we derive anomalous hydrodynamic equations from the point of view of quantum field theory. Assuming
Quantum Field Theory and Decoherence in the Early Universe
NASA Astrophysics Data System (ADS)
Koksma, J. F.
2011-06-01
Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop stress-energy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantum-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired
Field emission theory for an enhanced surface potential: a model for carbon field emitters
NASA Astrophysics Data System (ADS)
Choy, T. C.; Harker, A. H.; Stoneham, A. M.
2004-02-01
We propose a non-JWKB-based theory of electron field emission for carbon field emitters in which, for electrons with energy in the vicinity of the order of ϑ to the Fermi level, the effective (1/x) surface potential is strongly enhanced. The model grossly violates the WKB validity criteria and necessitates an analytic treatment of the one-dimensional Schrödinger equation, which we first obtain. We determine ϑ (which is field-dependent) from the wavefunction matching point close to the surface. For reasonable values of the surface parameters—work function \\varphi \\approx 2 -5 eV, electron affinity \\chi \\approx 2 \\varphi and an empirical electron loss factor \\sigma \\approx 10^{-3} (and with no other adjustable parameters)—the theory provides an intriguing agreement with experimental data from carbon epoxy graphite composite (PFE) and certain graphitized carbon nanotube field emitters. We speculate on the surface potential enhancement, which can be interpreted as a massive (field-induced) dielectric effect of dynamic origin. This can be related via time-dependent perturbation theory to second-order non-linear polarizability enhancements at ultraviolet {\\sim }3000~\\AA wavelengths near the tunnelling region. Finally some exact mathematical results are included in the appendix for future reference.
NASA Astrophysics Data System (ADS)
Najima, R.; Hiroki, A.; Kawasaki, S.; Kimura, T.
1986-01-01
Gauge theories of antisymmetric tensor-spinor fields of higher ranks are investigated. The manifestly covariant BRS and anti-BRS invariant theories of these spinor gauge fields are formulated in Bonora and Tonin's superspace formalism.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Dissipative quantum transport in macromolecules: Effective field theory approach
NASA Astrophysics Data System (ADS)
Schneider, E.; a Beccara, S.; Faccioli, P.
2013-08-01
We introduce an atomistic approach to the dissipative quantum dynamics of charged or neutral excitations propagating through macromolecular systems. Using the Feynman-Vernon path integral formalism, we analytically trace out from the density matrix the atomic coordinates and the heat bath degrees of freedom. This way we obtain an effective field theory which describes the real-time evolution of the quantum excitation and is fully consistent with the fluctuation-dissipation relation. The main advantage of the field-theoretic approach is that it allows us to avoid using the Keldysh contour formulation. This simplification makes it straightforward to derive Feynman diagrams to analytically compute the effects of the interaction of the propagating quantum excitation with the heat bath and with the molecular atomic vibrations. For illustration purposes, we apply this formalism to investigate the loss of quantum coherence of holes propagating through a poly(3-alkylthiophene) polymer.
Magnetic properties of a nanoribbon: An effective-field theory
NASA Astrophysics Data System (ADS)
Wang, Jiu-Ming; Jiang, Wei; Zhou, Chen-Long; Shi, Zuo; Wu, Chuang
2017-02-01
An effective-field theory is proposed to study magnetic properties of a nanoribbon. The model consists of a core spin-3/2 and shell spin-2 with a ferrimagnetic exchange coupling, which is described by transverse Ising model with the anisotropy. Based on the differential operator technique, the magnetization and the susceptibility formulas of the nanoribbon are given. Numerical results of the magnetization, the susceptibility, the hysteresis loop of the system are discussed for specific values of the parameters. Magnetization plateaus exhibits on the magnetization curves at low temperature. The exchange coupling, the anisotropy and the transverse field have important roles in the magnetic properties for the nanoribbon. Results may provide some guidance to design in the nanoribbons.
TOPICAL REVIEW: Modelling polycrystalline solidification using phase field theory
NASA Astrophysics Data System (ADS)
Gránásy, László; Pusztai, Tamás; Warren, James A.
2004-10-01
We review recent advances made in the phase field modelling of polycrystalline solidification. Areas covered include the development of theory from early approaches that allow for only a few crystal orientations, to the latest models relying on a continuous orientation field and a free energy functional that is invariant to the rotation of the laboratory frame. We discuss a variety of phenomena, including homogeneous nucleation and competitive growth of crystalline particles having different crystal orientations, the kinetics of crystallization, grain boundary dynamics, and the formation of complex polycrystalline growth morphologies including disordered ('dizzy') dendrites, spherulites, fractal-like polycrystalline aggregates, etc. Finally, we extend the approach by incorporating walls, and explore phenomena such as heterogeneous nucleation, particle-front interaction, and solidification in confined geometries (in channels or porous media).
On truncated generalized Gibbs ensembles in the Ising field theory
NASA Astrophysics Data System (ADS)
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2017-01-01
We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green’s function G(x)=< {{\\psi}\\dagger}(x)\\psi (0)> of the complex fermion field \\psi (x) . We find that both truncated GGEs are able to recover G(x), but for a given number of charges the semi-local version performs better.
Estimation of probability densities using scale-free field theories.
Kinney, Justin B
2014-07-01
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe results that allow this field-theoretic approach to be rapidly and deterministically computed in low dimensions, making it practical for use in day-to-day data analysis. Importantly, this approach does not impose a privileged length scale for smoothness of the inferred probability density, but rather learns a natural length scale from the data due to the tradeoff between goodness of fit and an Occam factor. Open source software implementing this method in one and two dimensions is provided.
The Unruh effect for higher derivative field theory
NASA Astrophysics Data System (ADS)
Berra-Montiel, Jasel; Martínez–Montoya, Jairo; Molgado, Alberto
2017-04-01
We analyse the emergence of the Unruh effect within the context of a field Lagrangian theory associated with the Pais–Uhlenbeck fourth order oscillator model. To this end, we introduce a transformation that brings the Hamiltonian bounded from below and is consistent with PT -symmetric quantum mechanics. We find that, as far as we consider different frequencies within the Pais–Uhlenbeck model, a particle together with an antiparticle of different masses are created and may be traced back to the Bogoliubov transformation associated with the interaction between the Unruh–DeWitt detector and the higher derivative scalar field. In contrast, whenever we consider the equal frequencies limit, no particle creation is detected as the pair particle/antiparticle annihilate each other. Further, following Moschella and Schaeffer, we construct a Poincaré invariant two-point function for the Pais–Uhlenbeck model, which in turn allows us to perform the thermal analysis for any of the emanant particles.
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.
Estimation of probability densities using scale-free field theories
NASA Astrophysics Data System (ADS)
Kinney, Justin B.
2014-07-01
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe results that allow this field-theoretic approach to be rapidly and deterministically computed in low dimensions, making it practical for use in day-to-day data analysis. Importantly, this approach does not impose a privileged length scale for smoothness of the inferred probability density, but rather learns a natural length scale from the data due to the tradeoff between goodness of fit and an Occam factor. Open source software implementing this method in one and two dimensions is provided.
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.
Bias in the effective field theory of large scale structures
Senatore, Leonardo
2015-11-05
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. Furthermore, we describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/k_{NL} and k/k_{M}, where k is the wavenumber of interest, k_{NL} is the wavenumber associated to the non-linear scale, and k_{M} is the comoving wavenumber enclosing the mass of a galaxy.
Bias in the effective field theory of large scale structures
Senatore, Leonardo
2015-11-05
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local inmore » space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. Furthermore, we describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/kNL and k/kM, where k is the wavenumber of interest, kNL is the wavenumber associated to the non-linear scale, and kM is the comoving wavenumber enclosing the mass of a galaxy.« less
The Gaussian streaming model and convolution Lagrangian effective field theory
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
Bias in the effective field theory of large scale structures
Senatore, Leonardo
2015-11-01
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/k{sub NL} and k/k{sub M}, where k is the wavenumber of interest, k{sub NL} is the wavenumber associated to the non-linear scale, and k{sub M} is the comoving wavenumber enclosing the mass of a galaxy.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
NASA Astrophysics Data System (ADS)
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
Behavior in strong fields of Euclidean gauge theories. II
NASA Astrophysics Data System (ADS)
Haba, Z.
1984-04-01
Functional determinants resulting from functional integration in quantum gauge theories are studied. We derive an expansion around the constant field strength for the (renormalized) spinor determinant detMF in QED. We show that, if the field strength F is large and its derivatives are bounded, then detMF≡exp(-W)~exp(cF2lnF2), where c>0. Hence, the effective action W in (four-dimensional) QED is unbounded from below. Moreover, we prove that exp(-W) is not integrable. A similar result is established in the Yukawa model [detMY~exp(φ4lnφ4)]. We estimate the scalar determinant detMA2 for a non-Abelian gauge field. We show that (like in the Abelian case studied earlier) detMA2=exp[c|F|2ln|F|2+r2(F,DF,DDF)], where c>0 and r2 is bounded by a quadratic form of the gauge-invariant variables |F|, |DF|, and |DDF|. We investigate the effect of gluon self-interaction on the stability of models with broken gauge symmetry G-->H (we discuss in detail the Georgi-Glashow model). We sum up (in an approximation) the contribution of massive gluons to the O(2)-invariant effective action. It is shown that this effective action is bounded from below for slowly varying fields, if the couplings are asymptotically free at the one-loop level.
Aspects of renormalization in finite-density field theory
Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia
2015-05-26
We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.
Multiagent model and mean field theory of complex auction dynamics
NASA Astrophysics Data System (ADS)
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
2015-09-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
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.
Effective field theory of weakly coupled inflationary models
Gwyn, Rhiannon; Palma, Gonzalo A.; Sakellariadou, Mairi; Sypsas, Spyros E-mail: gpalmaquilod@ing.uchile.cl E-mail: spyridon.sypsas@kcl.ac.uk
2013-04-01
The application of Effective Field Theory (EFT) methods to inflation has taken a central role in our current understanding of the very early universe. The EFT perspective has been particularly useful in analyzing the self-interactions determining the evolution of co-moving curvature perturbations (Goldstone boson modes) and their influence on low-energy observables. However, the standard EFT formalism, to lowest order in spacetime differential operators, does not provide the most general parametrization of a theory that remains weakly coupled throughout the entire low-energy regime. Here we study the EFT formulation by including spacetime differential operators implying a scale dependence of the Goldstone boson self-interactions and its dispersion relation. These operators are shown to arise naturally from the low-energy interaction of the Goldstone boson with heavy fields that have been integrated out. We find that the EFT then stays weakly coupled all the way up to the cutoff scale at which ultraviolet degrees of freedom become operative. This opens up a regime of new physics where the dispersion relation is dominated by a quadratic dependence on the momentum ω ∼ p{sup 2}. In addition, provided that modes crossed the Hubble scale within this energy range, the predictions of inflationary observables — including non-Gaussian signatures — are significantly affected by the new scales characterizing it.
The effectiveness of mean-field theory for avalanche distributions
NASA Astrophysics Data System (ADS)
Lee, Edward; Raju, Archishman; Sethna, James
We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.
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.
Towards strong field tests of beyond Horndeski gravity theories
NASA Astrophysics Data System (ADS)
Sakstein, Jeremy; Babichev, Eugeny; Koyama, Kazuya; Langlois, David; Saito, Ryo
2017-03-01
Theories of gravity in the beyond Horndeski class encompass a wide range of scalar-tensor theories that will be tested on cosmological scales over the coming decade. In this work, we investigate the possibility of testing them in the strong field regime by looking at the properties of compact objects—neutron, hyperon, and quark stars—embedded in an asymptotically de Sitter space-time, for a specific subclass of theories. We extend previous works to include slow rotation and find a relation between the dimensionless moment of inertia (I ¯ =I c2/GNM3 ) and the compactness C =GNM /R c2 (an I ¯-C relation), independent of the equation of state, that is reminiscent of but distinct from the general relativity prediction. Several of our equations of state contain hyperons and free quarks, allowing us to revisit the hyperon puzzle. We find that the maximum mass of hyperon stars can be larger than 2 M⊙ for small values of the beyond Horndeski parameter, thus providing a resolution of the hyperon puzzle based on modified gravity. Moreover, stable quark stars exist when hyperonic stars are unstable, which means that the phase transition from hyperon to quark stars is predicted just as in general relativity (GR), albeit with larger quark star masses. Two important and potentially observable consequences of some of the theories we consider are the existence of neutron stars in a range of masses significantly higher than in GR and I ¯-C relations that differ from their GR counterparts. In the former case, we find objects that, if observed, could not be accounted for in GR because they violate the usual GR causality condition. We end by discussing several difficult technical issues that remain to be addressed in order to reach more realistic predictions that may be tested using gravitational wave searches or neutron star observations.
Combinatorial Hopf Algebras in Quantum Field Theory I
NASA Astrophysics Data System (ADS)
Figueroa, Héctor; Gracia-Bondía, José M.
This paper stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an elementary invitation to the subject as well. The rest of Sec. 1 is devoted to the basics of Hopf algebra theory and examples in ascending level of complexity. Section 2 turns around the all-important Faà di Bruno Hopf algebra. Section 2.1 contains a first, direct approach to it. Section 2.2 gives applications of the Faà di Bruno algebra to quantum field theory and Lagrange reversion. Section 2.3 rederives the related Connes-Moscovici algebras. In Sec. 3, we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Sec. 3.1, we describe the first. Then in Sec. 3.2, we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Sec. 3.3, general incidence algebras are introduced, and the Faà di Bruno bialgebras are described as incidence bialgebras. In Sec. 3.4, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained. The structure results for commutative Hopf algebras are found in Sec. 4. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.
Growth regulation of primary human keratinocytes by prostaglandin E receptor EP2 and EP3 subtypes.
Konger, R L; Malaviya, R; Pentland, A P
1998-02-04
We examined the contribution of specific EP receptors in regulating cell growth. By RT-PCR and northern hybridization, adult human keratinocytes express mRNA for three PGE2 receptor subtypes associated with cAMP signaling (EP2, EP3, and small amounts of EP4). In actively growing, non-confluent primary keratinocyte cultures, the EP2 and EP4 selective agonists, 11-deoxy PGE1 and 1-OH PGE1, caused complete reversal of indomethacin-induced growth inhibition. The EP3/EP2 agonist (misoprostol), and the EP1/EP2 agonist (17-phenyl trinor PGE2), showed less activity. Similar results were obtained with agonist-induced cAMP formation. The ability of exogenous dibutyryl cAMP to completely reverse indomethacin-induced growth inhibition support the conclusion that growth stimulation occurs via an EP2 and/or EP4 receptor-adenylyl cyclase coupled response. In contrast, activation of EP3 receptors by sulprostone, which is virtually devoid of agonist activity at EP2 or EP4 receptors, inhibited bromodeoxyuridine uptake in indomethacin-treated cells up to 30%. Although human EP3 receptor variants have been shown in other cell types to markedly inhibit cAMP formation via a pertussis toxin sensitive mechanisms, EP3 receptor activation and presumably growth inhibition was independent of adenylyl cyclase, suggesting activation of other signaling pathways.
Geometrical Effective Action: Gauge Field Theory Without Ghosts.
NASA Astrophysics Data System (ADS)
Paris, Carmen Molina
Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph. Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions^1, obtaining thereby a mode sum over tree functions. It is easy to show that tree functions are gauge invariant provided the external lines bear only physical mode functions. Feynman therefore proposed to restrict the mode sums to physical modes, a procedure that not only secures gauge invariance but unitarity as well. But there is a difficulty: Because the physical mode functions are defined in a special frame, the procedure is not manifestly Lorentz invariant ^2. Feynman was able to show that deletion of the nonphysical modes is equivalent to subtracting, from the contribution of every closed loop, that of another (Lorentz invariant) loop propagating a particle having spin 1 (or one less than that of the gauge field). This is the ghost. Because its contribution is subtracted, it is a fermion. Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show
Symmetries and quantum corrections in heavy quark effective field theory
NASA Astrophysics Data System (ADS)
McIrvin, Matthew James
1997-11-01
Finite-mass corrections to the Lagrangian of heavy quark effective field theory appear in a power series in the reciprocal of the quark mass. The running of these terms' coefficients to order 1/m2 is calculated to one loop, continuously redefining the quark field to eliminate operators vanishing according to the leading- order equation of motion. Results are found to agree with other recent calculations, and with constraints implied by reparameterization invariance. Different forms for the reparameterization transformation have appeared in the literature. A field redefinition is discussed which reveals the equivalence, at the level of the S-matrix, of a large family of reparameterization transformations. To order 1/m2 in the Lagrangian, these give differing predictions only for operators vanishing by the leading- order equation of motion. A new, very straightforward proof of the reparameterization constraints, applicable to order 1/m2 but to all orders in αs, is described. The results are compared with two previously proposed versions of reparameterization invariance.
Effective field theory of non-attractor inflation
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra
2015-07-29
We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.
Effective field theory of non-attractor inflation
Akhshik, Mohammad; Jazayeri, Sadra; Firouzjahi, Hassan E-mail: firouz@ipm.ir
2015-07-01
We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.
Renormalizable Models in Rank Tensorial Group Field Theory
NASA Astrophysics Data System (ADS)
Geloun, Joseph Ben
2014-11-01
Classes of renormalizable models in the Tensorial Group Field Theory framework are investigated. The rank d tensor fields are defined over d copies of a group manifold or with no symmetry and no gauge invariance assumed on the fields. In particular, we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form . This study is tailored for models equipped with Laplacian dynamics on G D (case a = 1) but also for more exotic nonlocal models in quantum topology (case 0 < a < 1). A generic model can be written , where k is the maximal valence of its interactions. Using a multi-scale analysis for the generic situation, we identify several classes of renormalizable actions, including matrix model actions. In this specific instance, we find a tower of renormalizable matrix models parametrized by . In a second part of this work, we study the UV behavior of the models up to maximal valence of interaction k = 6. All rank tensor models proved renormalizable are asymptotically free in the UV. All matrix models with k = 4 have a vanishing β-function at one-loop and, very likely, reproduce the same feature of the Grosse-Wulkenhaar model (Commun Math Phys 256:305, 2005).
a Unified Formalism of Thermal Quantum Field Theory
NASA Astrophysics Data System (ADS)
Chu, H.; Umezawa, H.
We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.
Improved routing strategy based on gravitational field theory
NASA Astrophysics Data System (ADS)
Song, Hai-Quan; Guo, Jin
2015-10-01
Routing and path selection are crucial for many communication and logistic applications. We study the interaction between nodes and packets and establish a simple model for describing the attraction of the node to the packet in transmission process by using the gravitational field theory, considering the real and potential congestion of the nodes. On the basis of this model, we propose a gravitational field routing strategy that considers the attractions of all of the nodes on the travel path to the packet. In order to illustrate the efficiency of proposed routing algorithm, we introduce the order parameter to measure the throughput of the network by the critical value of phase transition from a free flow phase to a congested phase, and study the distribution of betweenness centrality and traffic jam. Simulations show that, compared with the shortest path routing strategy, the gravitational field routing strategy considerably enhances the throughput of the network and balances the traffic load, and nearly all of the nodes are used efficiently. Project supported by the Technology and Development Research Project of China Railway Corporation (Grant No. 2012X007-D) and the Key Program of Technology and Development Research Foundation of China Railway Corporation (Grant No. 2012X003-A).
Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory
Wohlfeld, K.; Chen, Cheng-Chien; van Veenendaal, M.; ...
2015-02-01
Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstancesmore » be regarded as more complex than the physics of a spin-orbital chain.« less