Advances In Classical Field Theory
Yahalom, Asher
2011-01-01
Classical field theory is employed by physicists to describe a wide variety of physical phenomena. These include electromagnetism, fluid dynamics, gravitation and quantum mechanics. The central entity of field theory is the field which is usually a multi component function of space and time. Those multi component functions are usually grouped together as vector fields as in the case in electromagnetic theory and fluid dynamics, in other cases they are grouped as tensors as in theories of gravitation and yet in other cases they are grouped as complex functions as in the case of quantum mechanic
Three Approaches to Classical Thermal Field Theory
Gozzi, E.; Penco, R.
2010-01-01
In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the Closed-Time Path (CTP) formalism, the Thermofield Dynamics (TFD) and the Matsubara approach.
Three approaches to classical thermal field theory
Gozzi, E.; Penco, R.
2011-04-01
In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Classical-field theory of thermal radiation
Rashkovskiy, Sergey A
2016-01-01
In this paper, using the viewpoint that quantum mechanics can be constructed as a classical field theory without any quantization I build a fully classical theory of thermal radiation. Planck's law for the spectral energy density of thermal radiation and the Einstein A-coefficient for spontaneous emission are derived in the framework of classical field theory without using the concept of "photon". It is shown that the spectral energy density of thermal radiation is apparently not a universal function of frequency, as follows from the Planck's law, but depends weakly on the nature of atoms, while Planck's law is valid only as an approximation in the limit of weak excitation of atoms.
Classical theory of electric and magnetic fields
Good, Roland H
1971-01-01
Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma
The classical theory of fields electromagnetism
Helrich, Carl S
2012-01-01
The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Introduction to classical and quantum field theory
This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into three parts, the first part covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part introduces more advanced concepts and techniques. Part III discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing, 'real' physics problems. Throughout there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers. (orig.)
Classical solutions in quantum field theories
Quantum field theories are difficult to solve because they are governed by nonlinear operator equations. A one-dimensional example, termed the kink, is presented of a classical solution. Topological and nontopological solitons in more than one spatial dimension are also discussed. Euclidean solutions and barrier penetration are also reviewed, focusing on vacuum decay by tunneling, Yang-Mills Instantons, the physical consequences of vacuum tunneling, and thermal fluctuations and sphalerons. 119 refs., 2 figs
Momentum Maps and Classical Relativistic Fields; 1, Covariant Field Theory
Gotay, M J; Marsden, J E; Gotay, Mark J.; Isenberg, James; Marsden, Jerrold E.
1998-01-01
This is the first paper of a four part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge transformations in such theories (either relativistic or not). To do this, in the course of these four papers, we develop and use a number of tools from symplectic and multisymplectic geometry. Of central importance in our analysis is the notion of the ``energy-momentum map'' associated to the gauge group of a given classical field theory. We hope to demonstrate that many different and apparently unrelated facets of field theories can be thereby tied together and understood in an essentially new way. In Part I we develop some of the basic theory of classical fields from a spacetime covariant viewpoint. We begin with a study of the covariant Lagrangian and Hamiltonian formalisms, on jet bundles and multisymplectic manifolds, respectively. Then we discuss symmetries, conserva...
Conformal Invariance in Classical Field Theory
Grigore, D. R.
1993-01-01
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.
Classical Solutions in Quantum Field Theory
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
Lectures on Classical and Quantum Theory of Fields
Arodź, Henryk
2010-01-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.
Lectures on classical and quantum theory of fields
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)
Quantum fermions and quantum field theory from classical statistics
Wetterich, C.
2012-01-01
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schr\\"odinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.
Introduction to classical and quantum Lagrangian field theory. 9
The basic principles of relativistic Lagrangian field theory are introduced, first in the classical context and later in the quantized form. Various free fields are discussed, their quantization, Lorentz invariance and the important discrete symmetries. Going on to interacting quantum fields, the invariant perturbation theory and Feynman graphs are succinctly discussed. Renormalizability and renormalization methods are covered with emphasis on the method of dimensional regularization. (author).3 refs.; 7 figs
Classical electromagnetic field theory in the presence of magnetic sources
Chen, W J; Naón, C M; Chen, Wen-Jun; Li, Kang
2001-01-01
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.
Classical Electromagnetic Field Theory in the Presence of Magnetic Sources
LI Kang(李康); CHEN Wen-Jun(陈文俊); NAON Carlos M.
2003-01-01
Using two new well-defined four-dimensional potential vectors, we formulate the classical Maxwell field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources.We set up a consistent Lagrangian for the theory. Then from the action principle we obtain both Maxwell's equation and the equation of motion of a dyon moving in the electromagnetic field.
On the variational formulation of classical Abelian gauge field theories
It is shown how one can formulate an action principle for classical Abelian gauge theories not by means of gauge potentials and currents but in terms of the gauge invariant field strengths and gauge variant stream potentias. The discussion is on a general formal level in n=s+t space-time dimensions and uses, for brevity, the language of differential forms
Quantum to classical transition in quantum field theory
Lombardo, F C
1998-01-01
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the cri...
Quantum Mind from a Classical Field Theory of the Brain
Zizzi, Paola
2011-01-01
We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzatz for the gauge field, which breaks Lorentz invariance. In the ansatz, a contraction mapping plays the role of dissipation. In the limit of maximal dissipation, which corresponds to the attractive fixed point of the contraction mapping, the gauge fields reduce, up to constant factors, to the Pauli quantum gates for one-qubit states. Then tubuline-qubits can be processed in the quantum vacuum of the classical field theory of the brain, where decoherence is avoided due to the extremely low temperature. Finally, we interpret...
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
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
On Covariant Poisson Brackets in Classical Field Theory
Forger, Michael; Salles, Mário O.
2015-01-01
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem - as testified by the extensive literature on "multisymplectic Poisson brackets", together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls - De Witt bracket and whose construction in a geometrical setting is now well unde...
Wu, Ning; Zhang, Dahua
2005-01-01
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the Schwarzschild solution. In gauge theory of gravity, the equation of motion of a classical mass point in gravitational gauge field is given by Ne...
Motion of small bodies in classical field theory
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.
Local gauge invariant Lagrangeans in classical field theories
We investigate the most general local gauge invariant Lagrangean in the framework of classical field theory. We rederive esentially Utiyama's result with a slight generalization. Our proof makes clear the importance of the so called current conditions, i.e. the requirement that the Noether currents are different from zero. This condition is of importance both in the general motivation for the introduction of the Yang-Mills fields and for the actual proof. Some comments are made about the basic mathematical structure of the problem - the gauge group. (author)
Zatloukal, Václav
2016-04-01
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.
Gauge-fields and integrated quantum-classical theory
Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs
Lie Groupoids in Classical Field Theory I: Noether's Theorem
Costa, Bruno T; Pêgas, Luiz Henrique P
2015-01-01
In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.
Quasiperiodical orbits in the scalar classical lambdaphi4 field theory
New numerical and theoretical results of resonance kink-antikink (Kanti K) interactions in the classical one-dimentional space Higgs theory are presented. Earlier studies of these interactions revealed nine initial relative velocity-intervals with two-bounce Kanti K-collisions followed by the escape of kinks to infinite separations, the breathing solution was formed outside those intervals. Two-bounce Kanti K-interactions with the number of small oscillations between Kanti K-bounces up to 35 in the initial kink velocity interval 0.18 <= Vsub(infinite) <= 0.26 were found. Several examples for n-bounces Kanti K-interaction (n <= 6) are also found. The observed phenomenon can be explaned by the existence of quasi-two-periodical solutions of the nonlinear wave equation. The simple Hamiltonian with two degrees of freedom is studied. This model supplies quantitative descrtiptions of all numerical results for the field theory considered above. The considered phenomenon may be called ''autoquantization'' of a nonlinear classical scalar selfinteracting field
Geometry of Lagrangian first-order classical field theories
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)
Latfield2: A c++ library for classical lattice field theory
David, Daverio; Bevis, Neil
2015-01-01
latfield2 is a C++ library designed to simplify writing parallel codes for solving partial differen- tial equations, developed for application to classical field theories in particle physics and cosmology. It is a significant rewrite of the latfield framework, moving from a slab domain decomposition to a rod decomposition, where the last two dimension of the lattice are scattered into a two dimensional process grid. Parallelism is implemented using the Message Passing Interface (MPI) standard, and hidden in the basic objects of grid-based simulations: Lattice, Site and Field. It comes with an integrated parallel fast Fourier transform, and I/O server class permitting computation to continue during the writing of large files to disk. latfield2 has been used for production runs on tens of thousands of processor elements, and is expected to be scalable to hundreds of thousands.
Geometry of Lagrangian first-order classical field theories
Echeverria-Enriquez, A. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Munoz-Lecanda, M.C. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Roman-Roy, N. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica
1996-10-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether`s theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Quantum Mind from a Classical Field Theory of the Brain
Zizzi, Paola
2011-01-01
We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzat...
On covariant Poisson brackets in classical field theory
Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)
2015-10-15
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
On covariant Poisson brackets in classical field theory
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra
On covariant Poisson brackets in classical field theory
Forger, Michael; Salles, Mário O.
2015-10-01
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on "multisymplectic Poisson brackets," together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls-De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic "multisymplectic Poisson bracket" already proposed in the 1970s can be derived from the Peierls-De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
Restrictions imposed on relativistic two-body interactions by classical relativistic field theory
We show that various relativistic potential models (all sharing exact relativistic two-body kinematics and a common nonrelativistic limit) can be distinguished by agreement or disagreement with relativistic corrections produced by classical field theory. We find that the only one of these models whose relativisic corrections duplicate those of classical field theory is the minimal Todorov equation. Conversely, we derive the Todorov equation from the semirelativistic dynamics of classical field theory, thus exposing the classical field-theoretic origins of its characteristic minimal potential structures and dependences on effective one-body variables
The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity
A course in mathematical physics 2 classical field theory
Thirring, Walter
1978-01-01
In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in corporating the interesting developments in Kal...
Qian, Xiao-Feng; Howell, John C; Eberly, J H
2015-01-01
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schr\\"odinger's famous remark about it [Proc. Camb. Phil. Soc. {\\bf 31}, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than ${\\cal B} = 2.54$. This is many standard deviations outside the limit ${\\cal B} = 2$ established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. {\\bf 23}, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit ${\\cal B} = 2.828...$. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.
Quantum Electrodynamics Basis of Classical-Field High-Harmonic Generation Theory
王兵兵; 高靓辉; 傅盘铭; 郭东升; R. R. Freeman
2001-01-01
From the nonperturbative quantum electrodynamics theory, we derive the Landau-Dykhne formula which represents the quantum-mechanical formulation of the three-step model. These studies provide a basis for the classical-field approaches to high-order harmonic generation and justify some assumptions used in classical-field modelling.
The Poisson algebra of classical Hamiltonians in field theory and the problem of its quantization
Stoyanovsky, A.
2010-01-01
We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum algebra.
Zarei, Mohammad Hossein
2016-01-01
Although creating a unified theory in Elementary Particles Physics is still an open problem, there are a lot of attempts for unifying other fields of physics. Following such unifications, we regard a two dimensional (2D) classical $\\Phi^{4}$ field theory model to study several field theories with different symmetries in various dimensions. While the completeness of this model has been already proved by a mapping between statistical mechanics and quantum information theory, here, we take into account a fundamental systematic approach with purely mathematical basis to re-derive such completeness in a general manner. Due to simplicity and generality, we believe that our method leads to a general approach which can be understood by other physical communities as well as quantum information theorists. Furthermore, our proof of the completeness is not only a proof-of-principle, but also an interesting algorithmic proof. We consider a discrete version of a general field theory as an arbitrary polynomial function of f...
k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner–Rusk formulation on classical mechanics.
Quantization, Classical and Quantum Field Theory and Theta - Functions
Tyurin, Andrey N.
2002-01-01
In the abelian case (the subject of several beautiful books) fixing some combinatorial structure (so called theta structure of level k) one obtains a special basis in the space of sections of canonical polarization powers over the jacobians. These sections can be presented as holomorphic functions on the "abelian Schottky space". This fact provides various applications of these concrete analytic formulas to the integrable systems, classical mechanics and PDE's. Our practical goal is to do the...
In this paper, a detailed numerical comparison of the high-harmonic generation (HHG) from free electrons in intense laser fields in both classical and semi-classical frameworks has been presented. These two frameworks have been widely used in the literature. It has been found that the HHG spectra display distinct quantitative differences for high-energy electrons. In some special situations, qualitative differences appear. Even if the radiation reaction is included in the electron classical dynamics, no consistent result can be obtained. Hence it should be of critical importance to submit the present HHG theory for high-precision experimental tests, which can help us not only to justify the present theories, but also to check the QED predictions in the high-intensity regime. (paper)
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Davidson, Ronald C
2015-01-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underly...
An analogue of the Heisenberg uncertainty relation in prequantum classical field theory
Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.
The Master Ward Identity and generalized Schwinger-Dyson Equation in classical field theory
In the framework of perturbative quantum field theory a new, universal renormalization condition (called Master Ward Identity) was recently proposed by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the present paper is to get a better understanding of the Master Ward Identity by analyzing its meaning in classical field theory. It turns out that it is the most general identity for classical local fields which follows from the field equations. It is equivalent to a generalization of the Schwinger-Dyson Equation and is closely related to the Quantum Action Principle of Lowenstein and Lam. The validity of the Master Ward Identity makes possible a local construction of quantum gauge theories. (orig.)
Kuwahara, Y.; Nakamura, Y.; Yamanaka, Y.
2013-12-01
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [1]. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Kuwahara, Y., E-mail: a.kuwahara1224@asagi.waseda.jp; Nakamura, Y., E-mail: nakamura@aoni.waseda.jp; Yamanaka, Y., E-mail: yamanaka@waseda.jp
2013-12-09
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Kuwahara, Y; Nakamura, Y; Yamanaka, Y
2013-01-01
The $2 \\times 2$-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [Phys. Rev. Lett. 110, 174301 (2013)]. We show that the Galley's Hamilto...
Two-Component Theory of Classical Proca Fields in Curved Spacetimes with Torsionless Affinities
Santos Júnior, S. I.; Cardoso, J. G.
2016-04-01
The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is reviewed. Subsequently the entire set of field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are ultimately carried by the wave equations at issue. What results is, in effect, that the only interactions which occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.
A course in mathematical physics 1 and 2 classical dynamical systems and classical field theory
Thirring, Walter
1992-01-01
The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap ter with the proof of the K-A-M Theorem to make allowances for the cur rent trend in physics. This involved not only the use of more refined mathe matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the ...
Motion in classical field theories and the foundations of the self-force problem
Harte, Abraham I
2014-01-01
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally ...
Sokolov, Igor V
2015-01-01
A theory of Symplectic Manifold with Contact Degeneracies (SMCD) was developed in [Zot'ev,2007]. The symplectic geometry uses an anti-symmetric tensor (closed differential form) such as a field tensor used in the classical field theory. The SMCD theory studies degeneracies of such form. In [Zot'ev,2011] the SMCD theory was applied to study a front of an electromagnetic pulsed field propagating into a region with no field. Here, the result of [Zot'ev,2011] is compared with the problem solution obtained using the well-known method presented in Witham, G.B., Linear and nonlinear waves, 1974. It is shown that the SMCD theory prediction is not supported by the result obtained with the Witham method.
The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Boedeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot φ4 theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society
Jalilian-Marian, J; Venugopalan, R; Wirstam, J; Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju; Wirstam, Jens
2000-01-01
The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Bödeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot $\\phi^4$ theory, and elucidate its relation to classical transport theory.
AMMARI, Zied; Falconi, Marco
2016-01-01
In the mid Sixties Edward Nelson proved the existence of a consistent quantum field theory that describes the Yukawa-like interaction of a non-relativistic nucleon field with a relativistic meson field. Since then it is thought, despite the renormalization procedure involved in the construction, that the quantum dynamics should be governed in the classical limit by a Schr\\"odinger-Klein-Gordon system with Yukawa coupling. In the present paper we prove this fact in the form of a Bohr correspon...
Classical and quantum effective theories
Polonyi, Janos
2014-01-01
A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.
On the Classical String Solutions and String/Field Theory Duality
Aleksandrova, D.; Bozhilov, P.
2003-01-01
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet time parameter.
Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Ryan eBabbush
2013-10-01
Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Numerical study of chiral plasma instability within the classical statistical field theory approach
Buividovich, P. V.; Ulybyshev, M. V.
2016-07-01
We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and noncompact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, the electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of the electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon, which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields that is not accompanied by the axial charge decay. This suggests that the relation between the inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.
Khrennikov, Andrei
2016-01-01
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\\"odinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be inaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity - the quantum state ("wave function"). The correspondence PCSFT to QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and th...
Relativistic and nonrelativistic classical field theory on fivedimensional space-time
This paper is a sequel to earlier ones in which, on the one hand, classical field theories were described on a curved Newtonian space-time, and on the other hand, the Newtonian gravitation theory was formulated on a fivedimensional space-time with a metric of signature and a covariantly constant vector field. Here we show that Lagrangians for matter fields are easily formulated on this extended space-time from simple invariance arguments and that stress-energy tensors can be derived from them in the usual manner so that four-dimensional space-time expressions are obtained that are consistent in the relativistic as well as in the Newtonian case. In the former the theory is equivalent to General Relativity. When the magnitude of the distinguished vector field vanishes equations for the (covariant) Newtonian limit follow. We demonstrate this here explicity in the case of the Klein-Gordon/Schroedinger and the Dirac field and its covariant nonrelativistic analogue, the Levy-Leblond field. Especially in the latter example the covariant Newtonian theory simplifies dramatically in this fivedimensional form
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong [PPPL; Burby, Joshua W [PPPL; Davidson, Ronald C [PPPL
2014-10-01
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Axiomatics of classical electrodynamics and its relation to gauge field theory
Gronwald, F; Nitsch, J; Gronwald, Frank; Hehl, Friedrich W.
2005-01-01
We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The {\\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.
Current-carrying plasma and the magnetic field ambiguity in classical MHD theory
An ambiguity in the classical theoretical framework used for computing magnetohydrostatic equilibrium is pointed out and analyzed. This inconsistency implies that some proposed solutions of the magnetohydrodynamic (MHD) equations may not represent actual magnetic fields of plasma currents in the geometry considered. The root of the inconsistency is that the magnetostatic field equation and the magnetohydrostatic equations are not invariant under the same transformations. There are two types of problems where inconsistencies have arisen in the literature: (a) unphysical magnetic fields are postulated inside a plasma current; and (b) vacuum magnetic fields are postulated that are not gradient fields. In both cases, magnetic fields are obtained which cannot be created in the laboratory. This inconsistency is traced back to a mishandling of the mathematical structure of the magnetic field equation. The magnetic field rvec B is a vector potential for the current density distribution rvec j, just as rvec A is a vector potential for rvec B. Nevertheless, whereas a gauge transformation on rvec A is unobservable (gauge invariant), the analogous gauge transformation in the rvec B vector (gradient field transformation) is indeed observable and changes the Lorentz force. Following Alfven, the authors characterize plasmas mathematically through the field lines of the current density distribution vector. Classical MHD theory, by contrast, is concerned strictly with magnetic field lines. They show here how this magnetic field approach can lead to inconsistencies when applied to plasmas. A resolution of entrenched ambiguities is made possible by using the current fiber description to derive a corrected Grad-Shafranov plasma equilibrium equation
A New Semi-Symmetric Uniﬁed Field Theory of the Classical Fields of Gravity and Electromagnetism
Suhendro I.
2007-10-01
Full Text Available We attempt to present a classical theoretical framework in which the gravitational and electromagnetic fields are unified as intrinsic geometric objects in the space-time manifold. For this purpose, we first present the preliminary geometric considerations dealing with the metric differential geometry of Cartan connections. The unified field theory is then developed as an extension of the general theory of relativity based on a semi- symmetric Cartan connection which is meant to be as close as possible structurally to the symmetric connection of the Einstein-Riemann space-time.
Classical solutions in quantum field theory solitons and instantons in high energy physics
Weinberg, Erick J
2012-01-01
Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...
Mahajan, Gaurang
2007-01-01
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parametrize the wave function in terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions -- like those of particle number density, effective Lagrangian etc., which are usually defined using asymptotic in-out states -- are generalized as time-dependent concepts and we show that these generalized definitions lead to useful and reasonable results. Having developed the general formalism we apply it to several examples. Exact analytic expressions are found ...
Classical and quantum theory of the massive spin-two field
Koenigstein, Adrian; Giacosa, Francesco; Rischke, Dirk H.
2016-05-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers JPC =2-+ is, to our knowledge, given here for the first time.
Classical and quantum theory of the massive spin-two field
Koenigstein, Adrian; Rischke, Dirk H
2015-01-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincar\\'{e} group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers $J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.
Bruneton, Jean-Philippe
2006-01-01
Field theories whose full action is Lorentz invariant (or diffeomorphism invariant) can exhibit superluminal behaviors through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagations is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories, and we stress the rol...
Open and Closed String field theory interpreted in classical Algebraic Topology
Sullivan, Dennis
2003-01-01
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.
Classical theory of algebraic numbers
Ribenboim, Paulo
2001-01-01
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...
Gauge bridges in classical field theory; Eichbruecken in der klassischen Feldtheorie
Jakobs, S.
2009-03-15
In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called 'gauge bridges'are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)
Notes on Collective Field Theory of Large N Vector Models as Classical Mechanics on the Siegel Disc
Agarwal, A
2004-01-01
We use deformation quantization to construct the large N limits of Bosonic vector models as classical dynamical systems on the Siegel disc and study the relation of this formulation to standard results of collective field theory. Special emphasis is paid to relating the collective potential of the large N theory to a particular cocycle of the symplectic group.
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
Non-Noetherian symmetries for oscillators in classical mechanics and in field theory
Hojman, Sergio A.; Delajara, Jamie; Pena, Leda
1995-01-01
Infinitely many new conservation laws both for free fields as well as for test fields evolving on a given gravitational background are presented. The conserved currents are constructed using the field theoretical counterpart of a recently discovered non-Noetherian symmetry which gives rise to a new way of solving the classical small oscillations problem. Several examples are discussed.
Classical isodual theory of antimatter
Santilli, R M
1997-01-01
An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatments of matter and antimatter in due time, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with expected images at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is anti-automorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also anti-automorphic, yet it is applicable beginning at the classical level and then persists at the quantum level. As part of our study, we present novel anti-isomorphic isodual images of the Galilean, special and general relativities and show the compatibility of their representation of antimatter with all available classical experi...
Múnera, Héctor A.
2016-07-01
It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger's first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich's unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.
WU Ning; ZHANG Da-Hua
2007-01-01
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field.First,by using Mathematica,a spherical symmetric solution of the field equation of gravitational gauge field is obtained,which is just the traditional Schwarzschild solution.Combining the principle of gauge covariance and Newton's second law of motion,the equation of motion of a mass point in gravitational field is deduced.Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field,we can discuss classical tests of gauge theory of gravity,including the deflection of light by the sun,the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun.It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
Equations of motion in Double Field Theory: from classical particles to quantum cosmology
Kan, Nahomi; Shiraishi, Kiyoshi
2012-01-01
The equation of motion for a point particle in the background field of double field theory is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by analysis on the particle motion, we propose a modified model of quantum string cosmology, which includes two scale factors. The report is based on Phys. Rev. D84 (2011) 124049 [arXiv:1108.5795].
Classical and quantum dynamics of two-dimensional nonlinear field theories: a review
Progress in understanding and solving a large class of two-dimensional nonlinear quantum field theories is reviewed. The discovery and development of the inverse scattering method for solving partial differential equations, and development of new perturbative methods are discussed. The generalized Bethe-ansatz method and its application to exactly diagonalize a fermionic problem are covered. 52 references
A Time-Dependent Classical Solution of C=1 String Field Theory and Non-Perturbative Effects
Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R.
1993-01-01
We describe a real-time classical solution of $c=1$ string field theory written in terms of the phase space density, $u(p,q,t)$, of the equivalent fermion theory. The solution corresponds to tunnelling of a single fermion above the filled fermi sea and leads to amplitudes that go as $\\exp(- C/ \\gst)$. We discuss how one can use this technique to describe non-perturbative effects in the Marinari-Parisi model. We also discuss implications of this type of solution for the two-dimensional black hole.
Field theories with Lorentz (or diffeomorphism invariant) action can exhibit superluminal behavior through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagation is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories and stress the role played by the Cauchy problem and the notion of chronology. We show that, in general, superluminal behavior threatens causality only if one assumes that a prior chronology in spacetime exists. In the case where superluminal propagation occurs, however, there are at least two nonconformally related metrics in spacetime and thus two available notions of chronology. These two chronologies are on equal footing, and it would thus be misleading to choose ab initio one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue that this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. In that framework, then, it is shown that superluminal propagation is not necessarily noncausal, the final answer depending on the existence of an initial data formulation. This also depends on global properties of spacetime that we discuss in detail. As an illustration of these conceptual issues, we consider two field theories, namely, k-essence scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, modified-Newtonian-dynamics-like theories of gravity, and varying speed of light theories
What can we learn from the classical theory of Yang-Mills and Dirac fields
Minimally coupled classical Yang-Mills and Dirac fields in the Minkowski space-time and in spatially bounded domains are investigated. The extended phase space, defined as the space of the Cauchy data admitting solutions of the evolution equations, is identified. The structure of the gauge symmetry group, defined as the group of all gauge transformations acting in the extended phase space is analysed. In the Minkowski space-time the Lie algebra of infinitesimal gauge symmetries has an ideal giving rise to the constraints. The quotient algebra, isomorphic to the structure algebra, labels the conserved colour charges. In the case of spatially bounded domains, each set of the boundary data gives rise to an extended phase space in which the evolution is Hamiltonian. The problem of a physical interpretation of the boundary data is discussed. (author)
Identity from classical invariant theory
A simple derivation is given of a well-known relation involving the so-called Cayley Operator of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics
FROM CLASSICAL TO EPISTEMIC GAME THEORY
ANDRÉS PEREA
2014-01-01
In this paper, we give a historical overview of the transition from classical game theory to epistemic game theory. To that purpose we will discuss how important notions such as reasoning about the opponents, belief hierarchies, common belief, and the concept of common belief in rationality arose, and gradually entered the game theoretic picture, thereby giving birth to the field of epistemic game theory. We will also address the question why it took game theory so long before it finally inco...
Classical theory of radiating strings
Copeland, Edmund J.; Haws, D.; Hindmarsh, M.
1990-01-01
The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.
Wrochna, Michał
2014-01-01
We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove it is isomorphic to the phase space in the subsidiary condition approach of Hack and Schenkel in the case of Maxwell, Yang-Mills, and Rarita-Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang-Mills case is concluded from known results in the subsidiary condition (or Gupta-Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang-Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.
Applications of classical detonation theory
Davis, W.C.
1994-09-01
Classical detonation theory is the basis for almost all calculations of explosive systems. One common type of calculation is of the detailed behavior of inert parts driven by explosive, predicting pressures, velocities, positions, densities, energies, etc as functions of time. Another common application of the theory is predicting the detonation state and expansion isentrope of a new explosive or mixtures, perhaps an explosive that has not yet been made. Both types of calculations are discussed.
Classical Theory of Hot-Electron Transport in Electric and Magnetic Fields
WENG Ming-Qi; WU Hang-Sheng
2002-01-01
Balance equation approach to the hot-electron transport in electric and magnetic fields is reformulated.The balance equations are re-derived from the Boltzmann equation. A new expression for the distribution function isreported in the present paper. It is homogeneous steady solution of the Boltzmann equation in constant relaxation timeapproximation. It holds when ωocτ < i or ωc < Te. As an example, the mobility of 2D electron gas in the GaAs-AlGaAsheterojunction is computed as a function of electric field and magnetic field.
Classical Theory of Hot－Electron Transport in Electric and Magnetic Fields
WENGMing－Qi; WuHang－Sheng
2002-01-01
Balance equation approach to the hot-electron transport in electric and magnetic fields is reformulated.The balance equations are re-derived from the Boltzmann equation.A new expression for the distribution function is reported in the present paper.It is homogeneous steady solution of the Boltzmann equation in costant relaxation time approximation.It holds when ωT<<1 or ωc<
The integral expressions for spectral-angular and spectral distributions of the radiation power of heterogeneous charged particles system moving on arbitrary trajectory in nonabsorbable isotropic media media with ε≠1 , μ≠1 are obtained using the Lorentz's self-interaction method. In this method a proper electromagnetic field, acting on electron, is defined as a semi difference between retarded and advanced potentials (Dirac, 1938). The power spectrum of Cherenkov radiation for the linear uniformly moving heterogeneous system of charged particles are obtained. It is found that the expression for the radiation power of heterogeneous system of charged particles becomes simplified when a system of charged particles is homogeneous. In this case the radiation power includes the coherent factor. It is shown what the redistribution effects in energy of the radiation spectrum of the studied system are caused by the coherent factor. The radiation spectrum of the system of electrons moving in a circle in this medium is discrete. The Doppler effect causes the appearance of the new harmonics for the system of electrons moving in a spiral. These harmonics form the region of continuous radiation spectrum. (authors)
Lagrangian formulation of classical BMT-theory
Full text: The most popular classical theory of electron has been formulated by Bargmann, Michel and Telegdi (BMT) in 1959. The BMT equations give classical relativistic description of a charged particle with spin and anomalous magnetic momentum moving in homogeneous electro-magnetic field. This allows to study spin dynamics of polarized beams in uniform fields. In particular, first experimental measurements of muon anomalous magnetic momentum were done using changing of helicity predicted by BMT equations. Surprisingly enough, a systematic formulation and the analysis of the BMT theory are absent in literature. In the present work we particularly fill this gap by deducing Lagrangian formulation (variational problem) for BMT equations. Various equivalent forms of Lagrangian will be discussed in details. An advantage of the obtained classical model is that the Lagrangian action describes a relativistic spinning particle without Grassmann variables, for both free and interacting cases. This implies also the possibility of canonical quantization. In the interacting case, an arbitrary electromagnetic background may be considered, which generalizes the BMT theory formulated to the case of homogeneous fields. The classical model has two local symmetries, which gives an interesting example of constrained classical dynamics. It is surprising, that the case of vanishing anomalous part of the magnetic momentum is naturally highlighted in our construction. (author)
Classical theory of the hydrogen atom
Rashkovskiy, Sergey
2016-01-01
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field, an "electron wave", which is held in a limited region of space by the electrostatic field of the proton. It is shown that quantum mechanics must be considered to be not a theory of particles but a classical field theory in the spirit of classical electrodynamics. In this case, we are not faced with difficulties in interpreting the results of the theory. In the framework of classical electrodynamics, all of the well-known regularities of the spontaneous emission of the hydrogen atom are obtained, which is usually derived in the framework of quantum electrodynamics. It is shown that there are no discrete states and discrete energy levels of the atom: the energy of the atom and its states change continuously. An explanation of the conventional corpuscular-statistical interpre...
The classical electromagnetic field
Eyges, Leonard
2010-01-01
This excellent text covers a year's course in advanced theoretical electromagnetism, first introducing theory, then its application. Topics include vectors D and H inside matter, conservation laws for energy, momentum, invariance, form invariance, covariance in special relativity, and more.
Confining properties of the classical SU(3) Yang - Mills theory
Dzhunushaliev, V D
1996-01-01
The spherically and cylindrically symmetric solutions of the $SU(3)$ Yang - Mills theory are obtained. The corresponding gauge potential has the confining properties. It is supposed that: a) the spherically symmetric solution is a field distribution of the classical ``quark'' and in this sense it is similar to the Coulomb potential; b) the cylindrically symmetric solution describes a classical field ``string'' (flux tube) between two ``quarks''. It is noticed that these solutions are typically for the classical $SU(3)$ Yang - Mills theory in contradiction to monopole that is an exceptional solution. This allows to conclude that the confining properties of the classical $SU(3)$ Yang - Mills theory are general properties of this theory.
Classical Electron Theory and Conservation Laws
Kiessling, Michael K. -H.
1999-01-01
It is shown that the traditional conservation laws for total charge, energy, linear and angular momentum, hold jointly in classical electron theory if and only if classical electron spin is included as dynamical degree of freedom.
Nielsen, H B; Nielsen, Holger B.; Ninomiya, Masao
2006-01-01
We consider a very complicated system of some latticized differential equations that is considered as equations of motion for a field theory. We define macro state restrictions for such a system analogous to thermodynamical states of a system in statistical mechanics. For the case in which we have assumed adiabaticity in a generalized way which is equivalent to reversible processes. It is shown that we can define various entropy currents, not only one. It is indeed surprising that, for a two dimensional example of lattice field theory, we get three different entropy currents, all conserved under the adiabaticity condition.
Extended phase space. I. Classical fields
Classical field theory is developed in the arena of extended phase space V8, the space of position, time, momentum, and energy. This enables one to incorporate Born's reciprocity which demands equal status for the variables q and p. The present formulation is covariant under the extended Poincare group P8 acting in V8. Variational methods for classical field theory are generalized. Besides the usual concept of the total 4-momentum, one encounters the notion of average position and time of the field distributions. The total charge emerges from a dynamical viewpoint. The Dirac and Duffin--Kemmer algebras are generalized in this setting. The corresponding wave equations would lead to a dynamical theory of the elementary particles. The symplectic structure is not considered because of the difficulties to represent spinors
Introduction to Classical Density Functional Theory by a Computational Experiment
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
Kleiss, Ronald H P
1999-01-01
In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.
We study the thermoelectric power under classically large magnetic field (TPM) in ultrathin films (UFs), quantum wires (QWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined III-V compounds form the special cases of our generalized analysis. The TPM has also been studied for quantum confined II-VI, stressed materials, bismuth and carbon nanotubes (CNs) on the basis of respective dispersion relations. It is found taking quantum confined CdGeAs2, InAs, InSb, CdS, stressed n-InSb and Bi that the TPM increases with increasing film thickness and decreasing electron statistics exhibiting quantized nature for all types of quantum confinement. The TPM in CNs exhibits oscillatory dependence with increasing carrier concentration and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of the TPM for non-degenerate materials having parabolic energy bands, leading to the compatibility test.
Classical Gauged Massless Rarita-Schwinger Fields
Adler, Stephen L
2015-01-01
We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields a consistent classical theory, with a generalized fermionic gauge invariance realized as a canonical transformation. To simplify the algebra, we study a two-component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. An analysis of Rarita-Schwinger spinor scattering from gauge fields shows that adiabatic decoupling fails in the limit of zero gauge field amplitude, invalidating various "no-go" theorems based on "on-shell" methods that claim to show the impossibility of gauging Rarita-Schwinger fields. Quantization of Rarita-Schwinger fields, using many formulas from this p...
This book is composed of 10 chapters. It starts by introducing classical principle of action. It adds quantal principle of action, which is divided into two cases that the degree of freedom is limited and limitless. It continues to basic quantum field theories, Green's function and functional differential equation toward green sources, solvable models, formal value of functional differential equation: quantization method of path integral formulation, approximate calculation of greens function, Representation Method of Schrodinger of quantum field theory and expansion of quantum field theory.
Bergshoeff, Eric A; Penas, Victor A; Riccioni, Fabio
2016-01-01
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
Functional Approach to Classical Yang-Mills Theories
Carta, P
2002-01-01
Sometime ago it was shown that the operatorial approach to classical mechanics, pioneered in the 30's by Koopman and von Neumann, can have a functional version. In this talk we will extend this functional approach to the case of classical field theories and in particular to the Yang-Mills ones. We shall show that the issues of gauge-fixing and Faddeev-Popov determinant arise also in this classical formalism.
Classical Electrodynamics in a Unified Theory
Ghose, Partha
2016-01-01
Some consequences of a fully classical unified theory of gravity and electromagnetism are worked out for the electromagnetic sector such as the occurrence of classical light beams with spin and orbital angular momenta that are topologically quantized in units of $q_e q_m=\\sigma$, independent of the beam size. Empirical fits require $\\sigma = \\hbar$. The theory also predicts a generalized coherency matrix whose consequences are testable.
Quantum feedback control and classical control theory
Doherty, Andrew C.; Habib, Salman; Jacobs, Kurt; Mabuchi, Hideo; Tan, Sze M.
1999-01-01
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential.
A Classical Introduction to Galois Theory
Newman, Stephen C
2012-01-01
This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematic
Beyond mean field theory: statistical field theory for neural networks
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. (paper)
Beam structures classical and advanced theories
Carrera, Erasmo; Petrolo, Marco
2011-01-01
Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for be
Introducing quantum effects in classical theories
Fabris, J C; Rodrigues, D C; Daouda, M H
2015-01-01
In this paper, we explore two different ways of implementing quantum effects in a classical structure. The first one is through an external field. The other one is modifying the classical conservation laws. In both cases, the consequences for the description of the evolution of the universe are discussed.
Prototype Theory and Classical Theory:An Explanation and Comparison
刘莹
2014-01-01
This paper discusses two different ways to understand categorization, which are classical theory and prototype theory. There is a deep exploration on how to understand categories, and different theoretical backgrounds of the two categorization the⁃ories. Furthermore, it reviews the limitations and advantages of both theories. And the comparison of the theories gives a clearer angle to understand their similarities and differences.
Eringen, A Cemal
1999-01-01
Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each volume element of a fluid in statistical mechanics is viewed as consisting of a large number of small particles for which statistical laws are valid. Classical continuum theories are valid when the characteristic length associated with external forces or stimuli is much larger than any internal scale of the body under consideration. When the characteristic lengths are comparable, however, the response of the individual constituents becomes important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balanc...
Emergence of classical theories from quantum mechanics
Hajicek, Petr
2012-01-01
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is ...
Relativistic Field Theory of Fluids
Jacques, Sylvan A.
2004-01-01
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current 4-vector and the electromagnetic field 2-form. The energy momentum tensor and equations of motion are derived from the fields. In this way the theory of continua is shown to have the same form as other field theories, such as electromagnetism and general relati...
Theory of interacting quantum fields
This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.
Studies in quantum field theory
Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD
Introduction to Classical Density Functional Theory by Computational Experiment
Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We present here an introductory practical course to classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely largely on nonintuitive abstract concepts and applied mathematics. They are nevertheless a powerful tool and an active field of research in physics and chemistry that led to the 1998 Nobel prize in chemistry. We here illustrate the DFT in its most mathematically simple and yet physically relevant form: the classical density functional theory of an ideal fluid in an external field, as applied to the prediction of the structure of liquid neon at the molecular scale. This introductory course is built around the production of a cDFT code written by students using the Mathematica language. In this way, they are brought to deal with (i) the cDFT theory itself, (ii) some basic concepts around the statistical mechanics of simple fluids, (iii) the underlying mathematical and numerical problem of functional minimization, and (iv) a functional programming languag...
"Scars" connect classical and quantum theory
Monteiro, T
1990-01-01
Chaotic systems are unstable and extremely sensitive to initial condititions. So far, scientists have been unable to demonstrate that the same kind of behaviour exists in quantum or microscopic systems. New connections have been discovered though between classical and quantum theory. One is the phenomena of 'scars' which cut through the wave function of a particle (1 page).
Topics in quantum field theory
This paper presents some important aspects on quantum field theory, covering the following aspects: the triumph and limitations of the quantum field theory; the field theory in curved spaces - Hawking and Unruh-Davies effects; the problem of divergent theory of the zero-point; the problem of the spinning detector and the Trocheries-Takeno vacuum; the field theory at finite temperature - symmetry breaking and phase transition; the problem of the summability of the perturbative series and the perturbative expansion for the strong coupling; quantized fields in presence of classical macroscopic structures; the Parisi-Wu stochastic quantization method
Satin, Seema
2015-01-01
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area...
On the tomographic description of classical fields
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so-called Gauss–Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
On the tomographic description of classical fields
Ibort, A., E-mail: albertoi@math.uc3m.es [Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid (Spain); López-Yela, A., E-mail: alyela@math.uc3m.es [Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.it [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Sudarshan, E.C.G., E-mail: bhamathig@gmail.com [Physics Department, Center for Particle Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, F., E-mail: ventriglia@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2012-03-26
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so-called Gauss–Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
On the tomographic description of classical fields
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Sudarshan, E C G; Ventriglia, F
2012-01-01
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so called Gauss--Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
Optimal search behavior and classic foraging theory
Random walk methods and diffusion theory pervaded ecological sciences as methods to analyze and describe animal movement. Consequently, statistical physics was mostly seen as a toolbox rather than as a conceptual framework that could contribute to theory on evolutionary biology and ecology. However, the existence of mechanistic relationships and feedbacks between behavioral processes and statistical patterns of movement suggests that, beyond movement quantification, statistical physics may prove to be an adequate framework to understand animal behavior across scales from an ecological and evolutionary perspective. Recently developed random search theory has served to critically re-evaluate classic ecological questions on animal foraging. For instance, during the last few years, there has been a growing debate on whether search behavior can include traits that improve success by optimizing random (stochastic) searches. Here, we stress the need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching. By sketching the assumptions of optimal foraging theory (OFT) and by summarizing recent results on random search strategies, we pinpoint ways to extend classic OFT, and integrate the study of search strategies and its main results into the more general theory of optimal foraging.
Classical and quantum electrodynamics and the B(3) field
Evans, Myron W
2001-01-01
It is well known that classical electrodynamics is riddled with internal inconsistencies springing from the fact that it is a linear, Abelian theory in which the potentials are unphysical. This volume offers a self-consistent hypothesis which removes some of these problems, as well as builds a framework on which linear and nonlinear optics are treated as a non-Abelian gauge field theory based on the emergence of the fundamental magnetizing field of radiation, the B(3) field. Contents: Interaction of Electromagnetic Radiation with One Fermion; The Field Equations of Classical O (3) b Electrodyn
Emergence of classical theories from quantum mechanics
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.
Emergence of classical theories from quantum mechanics
Hájíček, P.
2012-05-01
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.
Scheck, Florian [Mainz Univ. (Germany). Fachbereich Physik
2010-07-01
Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [German] Stringente Darstellung der Feldtheorie, vermittelt den Zusammenhang von der klassischen Elektrodynamik bis zu modernen Eichtheorien. Die kompakte Darstellung ist ideal fuer das Bachelor-Studium. Neues Kapitel zur Allgemeinen Relativitaetstheorie. Vertieft das Erlernte durch zahlreiche Anwendungsbeispiele aus Laserphysik, Metamaterialien uvm. Theoretische Physik 3. Klassische Feldtheorie. Von Elektrodynamik, nicht-Abelschen Eichtheorien und Gravitation ist der dritte von fuenf Baenden zur Theoretischen Physik von Professor Scheck. Der Zyklus Theoretische Physik umfasst: Band 1: Mechanik. Von den Newtonschen Gesetzen zum deterministischen Chaos. Band 2: Nichtrelativistische Quantentheorie. Vom Wasserstoffatom zu den Vielteilchensystemen. Band 3: Klassische Feldtheorie
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Dense matter theory a simple classical approach
Savic, P
1998-01-01
In the sixties,the first author and R.Kasanin have started developing a mean field theory of dense matter.This paper presents a short review of the basic ideas of the theory,and discusses some examples of its applications,which range from DAC experiments to modelling of planetary interiors.
A magnetic condensate solution of the classical electroweak theory
According to the electroweak theory a large homogeneous magnetic field exceeding m2w/e is unstable. We present a different solution of the classical electroweak field equations which is a condensate of magnetic fluxes induced by an anti-Lenz current of the charged vector bosons. The anti-Lenz mechanism is a consequence of asymptotic freedom. The range of validity of this solution depends on the Weinberg angle θ. (orig.)
CERN. Geneva; CERN. Geneva
2001-01-01
Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.
HCI Theory Classical, Modern, and Contemporary
Rogers, Yvonne
2012-01-01
Theory is the bedrock of many sciences, providing a rigorous method toadvance knowledge through testing and falsifying hypotheses aboutobservable phenomena. To begin with, the nascent field of HCI followedsuit, borrowing theories from cognitive science to test theories aboutuser performance at the interface.But HCI has emerged as an eclectic interdiscipline rather than a welldefinedscience. It now covers all aspects of human life, from birth tobereavement, through all manner of computing, from device ecologiesto nanotechnology. It comes as no surprise that the role of theory in HCIhas also gre
Classical gravity coupled to Liouville theory
We consider the two dimensional Jackiw-Teitelboim model of gravity. We first couple the model to the Liouville action and c scalar fields and show, treating the combined system as a non linear sigma model, that the resulting theory can be interpreted as a critical string moving in a target space of dimension D = c + 2. We then analyse perturbatively a generalized model containing a kinetic term and an arbitrary potential for the auxiliary field. We use the background field method and work covariant gauges. We show that the renormalizability of the theory depends on the form of the potential. For a general potential, the theory can be renormalized as a non linear sigma model. In the particular case of a Liouville-like potential, the theory is renormalized in the usual sense. (author). 31 refs
Classical gravity coupled to Liouville theory
We consider the two dimensional Jackiw-Teitelboim model of gravity. We first couple the model to the Liouville action and c scalar fields and show, treating the combined system as a non linear sigma model, that the resulting theory can be interpreted as a critical string moving in a target space of dimension D=c+2. We then analyze the model from a perturbative point of view. We show in particular that the results of conformal field theory are exactly reproduced at the one-loop level. We also show that the theory is one loop finite if the cosmological constant Λ is equal to zero. When Λ is different from zero the one loop divergences are gauge-fixing dependent even on-shell. However, the theory can be renormalized as a non linear sigma model if a kinetic term is included for the auxiliary field. (author). 27 refs
Differential formalism aspects of the gauge classical theories
The classical aspects of the gauge theories are shown using differential geometry as fundamental tool. Somme comments are done about Maxwell Electro-dynamics, classical Yang-Mills and gravitation theories. (L.C.)
Class field theory from theory to practice
Gras, Georges
2003-01-01
Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald-Wang theorem, Hilbert's towers,...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant (/cal T) p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book, intermediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory. In the corrected 2nd printing 2005, the author improves s...
Representational Realism, Closed Theories and the Quantum to Classical Limit
de Ronde, Christian
2016-01-01
In this paper we discuss the representational realist stance as a pluralist ontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two (Bohrian) metaphysical presuppositions -accepted in the present as dogmas that all interpretations must follow. We will also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the ...
Classical Ising chain in transverse field
The spin 12 Ising chain in transverse field is considered the prototypical system for quantum phase transitions. However, very little is apparently known in literature about its classical counterpart, not to be confused with the standard classical Ising model: while the latter is constructed from classical discrete variables, the model we consider is a chain of classical vectors of modulus 1, interacting via an Ising-like Hamiltonian. When an uniform field is applied perpendicular to the exchange interaction, both the quantum model and its classical counterpart get to be characterized by a critical field separating a ferromagnetically ordered state of minimal energy from a paramagnetic one. The properties of the classical model, and especially the behaviour of the correlation length, are investigated at low temperature around the critical field and compared with those of the quantum model, in order to single out the role played by quantum and classical fluctuations at finite temperature; the possibility to experimentally observe peculiar quantum critical effects in Ising spin chains is discussed
RELEVANCE OF CLASSICALAND NEO-CLASSICAL THEORIES IN PRESENT WORLD
Heena Kashyap
2015-01-01
This paper attempts to explain the impact of various management theories on Modern organisations. Primary purpose of this paper is to explain the relevance of studying Classical and Neo classical theories in the present world. Though these theories don’t consider external environmental changes in Management of Organisation, but they still hold significant place in present scenario. Classical and Neo Classical theories provide foundations for understanding continuous changes in ...
Classical theory of atomic collisions - The first hundred years
Grujić, Petar V.
2012-05-01
Classical calculations of the atomic processes started in 1911 with famous Rutherford's evaluation of the differential cross section for α particles scattered on foil atoms [1]. The success of these calculations was soon overshadowed by the rise of Quantum Mechanics in 1925 and its triumphal success in describing processes at the atomic and subatomic levels. It was generally recognized that the classical approach should be inadequate and it was neglected until 1953, when the famous paper by Gregory Wannier appeared, in which the threshold law for the single ionization cross section behaviour by electron impact was derived. All later calculations and experimental studies confirmed the law derived by purely classical theory. The next step was taken by Ian Percival and collaborators in 60s, who developed a general classical three-body computer code, which was used by many researchers in evaluating various atomic processes like ionization, excitation, detachment, dissociation, etc. Another approach was pursued by Michal Gryzinski from Warsaw, who started a far reaching programme for treating atomic particles and processes as purely classical objects [2]. Though often criticized for overestimating the domain of the classical theory, results of his group were able to match many experimental data. Belgrade group was pursuing the classical approach using both analytical and numerical calculations, studying a number of atomic collisions, in particular near-threshold processes. Riga group, lead by Modris Gailitis [3], contributed considerably to the field, as it was done by Valentin Ostrovsky and coworkers from Sanct Petersbourg, who developed powerful analytical methods within purely classical mechanics [4]. We shall make an overview of these approaches and show some of the remarkable results, which were subsequently confirmed by semiclassical and quantum mechanical calculations, as well as by the experimental evidence. Finally we discuss the theoretical and
Mathematical aspects of classical nonlinear field equations
In these notes we review some important advances in the mathematical analysis of classical nonlinear field equations. Our particular interest will be devoted to the nonlinear Schroedinger equation and the nonlinear Klein-Gordon equation. Since specifically nonlinear phenomena only become evident in the long-time behavior we are mainly concerned with global results rather than with solutions of these equations for a short time. We start with a thorough discussion of the nonlinear Schroedinger equation and its application to the theory of lasers and its bound states. In the following we study the general question of the existence of solutions of the nonlinear Klein-Gordon equation and other relativistic wave equations. The next section outlines the importance of the conservation laws which follow from the invariance properties of the equations. Special consideration is given to the Yang-Mills equations. The final section exposes a discussion of scattering theory mainly in the context of the nonlinear Klein-Gordon equation and summarizes the exciting development in recent years which has taken place in the nonlinear inverse scattering problem. (HJ)
Guerra, Francesco
2005-01-01
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical interpretation.
Polynomial Invariant Theory of the Classical Groups
Westrich, Quinton
2011-01-01
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \\emph{basic invariants}. In particular, we set out to find the set of basic invariants for the classical groups GL$(V)$, O$(n)$, and Sp$(n)$ for $n$ even. In the first half of the paper we set up relevant definitions and theorems for our search for the set of basic invariants, starting with linear algebraic groups and then discussing associative algebras. We then state and prove a monumental theorem that will allow us to proceed with hope: it says that the set of basic invariants is finite if $G$ is reductive. Finally we state without proof the First Fundamental Theorems, which aim to list explicitly the relevant sets of basic invariants, for the classical groups above. We end by commenting on some applications of invariant theory, on the history of its development, and stating a useful theorem in the appendix whose proof lies beyond the scope ...
Robust topological degeneracy of classical theories
Vaezi, Mohammad-Sadegh; Ortiz, Gerardo; Nussinov, Zohar
2016-05-01
We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display nonlocal entanglement. To this end, we introduce and study a classical rendition of the Toric Code model embedded on Riemann surfaces of different genus numbers. We find that the minimal ground state degeneracy (and those of all levels) depends on the topology of the embedding surface alone. As the ground states of this classical system may be distinguished by local measurements, a characteristic of Landau orders, this example illustrates that topological degeneracy is not a sufficient condition for topological quantum order. This conclusion is generic and, as shown, it applies to many other models. We also demonstrate that certain lattice realizations of these models, and other theories, display a ground state entropy (and those of all levels) that is "holographic", i.e., extensive in the system boundary. We find that clock and U (1 ) gauge theories display topological (in addition to gauge) degeneracies.
The classical pion field in a nucleus
Ripka, Georges
2007-01-01
A self-consistent symmetry arises when the nucleon angular momentum j and the isospin t are coupled to a grand spin G. Closed G shells become sources of a classical pion field with a hedgehog shape. Although the amplitude of the pion field, as measured by the chiral angle, is small, it is found to perturb significantly the energies of the nucleon orbits.
Classical-field description of the quantum effects in the light-atom interaction
Rashkovskiy, Sergey A
2016-01-01
In this paper I show that light-atom interaction can be described using purely classical field theory without any quantization. In particular, atom excitation by light that accounts for damping due to spontaneous emission is fully described in the framework of classical field theory. I show that three well-known laws of the photoelectric effect can also be derived and that all of its basic properties can be described within classical field theory.
An approximate classical unimolecular reaction rate theory
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Classical and Quantum Gauged Massless Rarita-Schwinger Fields
Adler, Stephen L
2015-01-01
We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields consistent classical and quantum theories. To simplify the algebra, we study a two component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. The quantized case is studied in covariant radiation gauge and axial gauge for the Rarita-Schwinger field, by both functional integral and Dirac bracket methods. The constraints have the form needed to apply the Faddeev-Popov method for deriving a functional integral in covariant radiation gauge. The Dirac bracket approach yields consistent Hamilton equations of motion in covariant radiation gauge, and leads to anticommutation rela...
Dynamics of classical and quantum fields an introduction
Setlur, Girish S
2014-01-01
Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. In-depth yet accessible, the book presents new and conventional topics in a self-contained manner that beginners would find useful. A partial list of topics covered includes: Geometrical meaning of Legendre transformation in classical mechanics Dynamical symmetries in the context of Noether's theorem The derivation of the stress energy tensor of the electromagnetic field, the expression for strain energy in elastic bodies, and the Navier Stokes equation Concepts of right and left movers in case of a Fermi gas explained Functional integration is interpreted as a limit of a sequence of ordinary integrations Path integrals for one and two quantum particles and for...
Bursa, Francis; Kroyter, Michael
2010-01-01
String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string field theory in a one dimensional linear dilaton background. We report the first results of our simulations.
Classical lifting processes and multiplicative vector fields
Mackenzie, Kirill; Xu, Ping
1997-01-01
We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a new description of the Lie bialgebroid structure associated with a Poisson groupoid.
Quantum Back Reaction on a Classical Field
Brout, R; Popescu, S; Parentani, R; Spindel, P; Spindel, Ph.
1995-01-01
We show how to apply post selection in the context of weak measurement of Aharonov and collaborators to construct the quantum back reaction on a classical field. The particular case which we study in this paper is pair creation in an external electric field and the back reaction is the counter field produced by the pair \\underline {as} it is made. The construction leads to a complex electric field obtained from non diagonal matrix elements of the current operator, the interpretation of which is clear in terms of weak measurement. The analogous construction applied to black hole physics (thereby leading to a complex metric) is relegated to a future paper.
Hilbert space theory of classical electrodynamics
RAJAGOPAL A K; GHOSE PARTHA
2016-06-01
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, {\\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.
Renormalizable Tensor Field Theories
Geloun, Joseph Ben
2016-01-01
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in any dimension and therefore form an interesting class of models for studying quantum gravity. We review the class of perturbatively renormalizable tensor field theories and some of their features.
The Jackiw-Pi model: Classical theory
Full text: One of the central problems in the framework of gauge field theories is the issue of gauge field mass. Gauge symmetry is not, in principle, conflicting with the presence of a massive gauge boson. In two space-time dimensions, the well-known Schwinger model puts in evidence the presence of a massive photon without the breaking of gauge symmetry. Another evidence for the compatibility between gauge symmetry and massive vector fields comes from the study of three-dimensional gauge theories. A topological mass term referred to as the Chern-Simons Lagrangian, once added to the Yang-Mills term, shifts the photon mass to a non-vanishing value without breaking gauge invariance, however parity symmetry is lost. In 1997, a massive even-parity non- Abelian gauge model in three space-time dimensions has been proposed by Jackiw and Pi, which is studied, at the tree-level, in this work. The propagators are computed and the spectrum consistency is analyzed, besides, the symmetries of the model are collected and established through BRS invariance and Slavnov-Taylor identity. In the Landau gauge, thanks to the antighost equations and the Slavnov-Taylor identity, two rigid symmetries are identified by means of Ward identities. It is presented here a promising path for perturbatively quantization of the Jackiw-Pi model and a hint concerning its possible quantum scale invariance is also pointed out. (author)
Number theory arising from finite fields analytic and probabilistic theory
Knopfmacher, John
2001-01-01
""Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory"" offers a discussion of the advances and developments in the field of number theory arising from finite fields. It emphasizes mean-value theorems of multiplicative functions, the theory of additive formulations, and the normal distribution of values from additive functions. The work explores calculations from classical stages to emerging discoveries in alternative abstract prime number theorems.
Covariant Noncommutative Field Theory
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
Field theories of quantum gravity
Attempts at constructing a satisfactory quantum field theory of gravity have been an active area of research for many years. We shall review various aspects of this problem restricting ourselves to the ''covariant'', rather than the ''canonical'', approach. This still leaves a vast area, and many interesting topics will have to be omitted. We discuss the violation of classical symmetries in quantum theory, i.e. the question of anomalies, and, in particular, gravitational anomalies; the ultraviolet problem in Einstein gravity and its supersymmetric extensions; the renormalizable ''higher derivative'' theory, and the status of the unitarity problem; and the further extension to strings, i.e. extended objects and infinite component field theories, and their ''low energy'' local field theory limit. (author)
Classical behavior of a scalar field in the inflationary universe
Extending the coarse-graining approach of Starobinsky, we formulate a theory to deal with the dynamics of a scalar field in inflationary universe models. We find a set of classical Langevin equations which describes the large scale behavior of the scalar field, provided that the coarse-grained size is greater than the effective compton wavelength of the scalar field. The corresponding Fokker-Planck equation is also derived which is defined on the phase space of the scalar field. We show that our theory is essentially equivalent to the one-loop field theory in de Sitter space and reduces to that of Starobinsky in a strong limit of the slow roll-over condition. Analysis of a simple Higgs potential model is done and the implications are discussed. (author)
Antigravity and classical solutions of five-dimensional Kaluza-Klein theory
Pollard, D. (Imperial Coll. of Science and Technology, London (UK). Blackett Lab.)
1983-02-21
Classical solutions are exhibited of a graviton-graviphoton-graviscalar field theory which are antigravitating in the weak-field approximation. The theory itself is obtained by a Kaluza-Klein type reduction from five to four dimensions. The solutions are dyonic black holes with scalar charge. They share some similarities with the extreme Reissner-Nordstrom black holes of Einstein-Maxwell theory.
The Possibility of Reconciling Quantum Mechanics with Classical Probability Theory
Slavnov, D. A.
2007-01-01
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.
A Quantum field theory of dyons
Lechner, K
1999-01-01
We construct a classical field theory action which upon quantization via thefunctional integral approach, gives rise to a consistent Dirac-stringindependent quantum field theory. The approach entails a systematic derivationof the correlators of all gauge invariant observables, and also of chargeddyonic fields. Manifest SO(2)-duality invariance and Lorentz invariance areensured by the PST-approach.
Classical solutions of some field theoretic models
In recent years much attention has been paid to simpler fields theories, so chosen that they possess several properties of nonabelian gauge theories. They preserve the conformal invariance of the action and one can define the topological charge for them. They possess nontrivial solutions to the equations of motion. The perturbation theory based on the fluctuations around each solution is characterized by asymptotic freedom. A model called CP sup(n-1) is presented and some models which are its natural generalizations are discussed. (M.F.W.)
Combinatorics and field theory
Bender, Carl M.; Brody, Dorje C.; Meister, Bernhard K.
2006-01-01
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph theory.
Classical theory of nonlinear Compton scattering
The covariant dynamics of a single electron subjected to the electromagnetic field of an intense, ultrashort laser pulse in vacuum is studied theoretically at arbitrary intensities, in the context of the Dirac-Lorentz equation, which has long been suggested as a possible theory including the radiative reaction due to the electron self-interaction. A brief review of the Lorentz-Maxwell electrodynamics including canonical invariants and scattered light spectra will be given, with a special emphasis on frequency modulation effects associated to the nonlinear relativistic Doppler shift induced by radiation pressure on the backscattered radiation. For circular polarization, an exact analytical expression for the full nonlinear spectrum is derived, and is presented. It is found that the scattering of coherent light by an electron describing a well-behaved trajectory can yield chaotic spectra when the laser ponderomotive force strongly modulates the electron's proper time. The Dirac-Lorentz equation is then derived and integrated numerically backward in time to ensure convergence towards the unique acausal solution satisfying the Dirac-Rohrlich asymptotic conditions (no runaway, law of inertia), and its consequences are investigated in terms of nonlinear Compton scattering. The relevance of this work to laser acceleration, as well as ongoing nonlinear Compton scattering experiments at SLAC and to the proposed γ-γ collider will also be discussed
Mathematical aspects of quantum field theory
de Faria, Edson
2010-01-01
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Field theory and the Standard Model
Dudas, E
2014-01-01
This brief introduction to Quantum Field Theory and the Standard Model con- tains the basic building blocks of perturbation theory in quantum field theory, an elementary introduction to gauge theories and the basic classical and quan- tum features of the electroweak sector of the Standard Model. Some details are given for the theoretical bias concerning the Higgs mass limits, as well as on obscure features of the Standard Model which motivate new physics con- structions
Non-linear coupling of quantum theory and classical gravity
The possibility that the non-linear evolution proposed earlier for a relativistic quantum field theory may be related to its coupling to a classical gravitational field is discussed. Formally, in the Schroedinger picture, it is shown how both the Schroedinger equation and Einstein's equations (with the expectation value of the energy-momentum tensor on the right) can be derived from a variational principle. This yields a non-linear quantum evolution. Other terms can be added to the action integral to incorporate explicit non-linearities of the type discussed previously. The possibility of giving a meaning to the resulting equation in a Heisenberg or interaction-like picture, is briefly discussed. (author)
A modification of Amiet's classical trailing edge noise theory for strictly two dimensional flows
Sandberg, Richard D.; Sandham, Neil D.
2007-01-01
The aim of this report is to derive theoretical expressions for the far-field pressure generated by disturbances convecting over a trailing edge. First, a general calculation of the far-field pressure is discussed. Then the classical theory of Amiet (1976b) is reviewed, listing the most relevant assumptions. Amiet's theory is then revised for two-dimensional flows.
A Tulczyjew triple for classical fields
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of the variational calculus, we construct the Tulczyjew triple for first-order field theory. The important feature of our approach is that we do not postulate ad hoc the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of field theory is covariant and complete, containing not only the Lagrangian formalism and Euler–Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps α and β which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We also discuss the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theory. (paper)
A Tulczyjew triple for classical fields
Grabowska, Katarzyna
2012-04-01
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of the variational calculus, we construct the Tulczyjew triple for first-order field theory. The important feature of our approach is that we do not postulate ad hoc the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of field theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps α and β which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We also discuss the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theory.
[Studies in quantum field theory
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity
Lange, Elizabeth
2015-01-01
This article argues that sociology has been a foundational discipline for the field of adult education, but it has been largely implicit, until recently. This article contextualizes classical theories of sociology within contemporary critiques, reviews the historical roots of sociology and then briefly introduces the classical theories…
Superspace conformal field theory
Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-07-15
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.
Superspace conformal field theory
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.
Classical conformality in the Standard Model from Coleman's theory
Kawana, Kiyoharu
2016-01-01
The classical conformality is one of the possible candidates for explaining the gauge hierarchy of the Standard Model. We show that it is naturally obtained from the Coleman's theory on baby universe.
Experimental assessment of unvalidated assumptions in classical plasticity theory.
Brannon, Rebecca Moss (University of Utah, Salt Lake City, UT); Burghardt, Jeffrey A. (University of Utah, Salt Lake City, UT); Bauer, Stephen J.; Bronowski, David R.
2009-01-01
This report investigates the validity of several key assumptions in classical plasticity theory regarding material response to changes in the loading direction. Three metals, two rock types, and one ceramic were subjected to non-standard loading directions, and the resulting strain response increments were displayed in Gudehus diagrams to illustrate the approximation error of classical plasticity theories. A rigorous mathematical framework for fitting classical theories to the data, thus quantifying the error, is provided. Further data analysis techniques are presented that allow testing for the effect of changes in loading direction without having to use a new sample and for inferring the yield normal and flow directions without having to measure the yield surface. Though the data are inconclusive, there is indication that classical, incrementally linear, plasticity theory may be inadequate over a certain range of loading directions. This range of loading directions also coincides with loading directions that are known to produce a physically inadmissible instability for any nonassociative plasticity model.
The hystory, main ideas, motivations for developing string field theory are reported. The connection between the first and second quantization for a system of point particles, strings and membranes is analysed. The main features of superstring theory are discussed. Free bosonic strings and string field algebra are considered
The semi classical laser theory and some applications of laser
The semi classical laser theory is concerned with the interaction between light and matter in such a way that the matter is treated quantum-mechanically whereas light is treated in terms of the classical electromagnetic equations. In this work the Maxwell-Bloch equations are employed to describe the interaction between light and matter. Applications of the theory as well as different types of lasers are reviewed. (Author)
Vibration of Timoshenko Beams Using Non-classical Elasticity Theories
J.V. Araújo dos Santos; J.N. Reddy
2012-01-01
This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theor...
We begin with a general discussion of topological field theories, their defining properties, and classification. The first model we consider in detail (section 3) is supersymmetric quantum mechanics. Topological sigma models, their observables, and the associated mathematics of complex geometry and intersection theory are presented in section 4. Following this, topological gauge theories are discussed in section 5, with particular emphasis on Donaldson theory. The matematics here is necessarily much more sophisticated than at any other point in this report, and to bridge this gap, a mathematical review of gauge theory and moduli spaces has been included. An analysis of the geometry underlying Donaldson theory gives a general recipe for constructing field theories associated to moduli spaces in arbitrary dimensions, and as an example, we analyze in detail the super BF theories associated with flat connections. Chern-Simons theory and related BF models are the subject of section 6. The connections with knot theory are briefly reviewed and the link with 2D conformal field theory is sketched. We also consider 3D gravity from the Chern-Simons point of view. A presentation of the metric and gauge theory approaches to topological gravity in two dimensions is given. As in all quantum field theories, the issues of renormalization needs to be addressed, and one is obliged to show that the formal topological properties of these theories survive quantization. This point is considered in section 8. We present a detailed analysis of the beta function in certain Witten type theories, and compute one-loop effects in Chern-Simons theory. (orig./HSI)
Birmingham, D. (CERN, Geneva (Switzerland). Theory Div.); Blau, M. (CNRS, 13 - Marseille (France). Centre de Physique Theorique NIKHEF-H, Amsterdam (Netherlands)); Rakowski, M.; Thompson, G. (Mainz Univ. (Germany). Inst. fuer Physik)
1991-12-01
We begin with a general discussion of topological field theories, their defining properties, and classification. The first model we consider in detail (section 3) is supersymmetric quantum mechanics. Topological sigma models, their observables, and the associated mathematics of complex geometry and intersection theory are presented in section 4. Following this, topological gauge theories are discussed in section 5, with particular emphasis on Donaldson theory. The matematics here is necessarily much more sophisticated than at any other point in this report, and to bridge this gap, a mathematical review of gauge theory and moduli spaces has been included. An analysis of the geometry underlying Donaldson theory gives a general recipe for constructing field theories associated to moduli spaces in arbitrary dimensions, and as an example, we analyze in detail the super BF theories associated with flat connections. Chern-Simons theory and related BF models are the subject of section 6. The connections with knot theory are briefly reviewed and the link with 2D conformal field theory is sketched. We also consider 3D gravity from the Chern-Simons point of view. A presentation of the metric and gauge theory approaches to topological gravity in two dimensions is given. As in all quantum field theories, the issues of renormalization needs to be addressed, and one is obliged to show that the formal topological properties of these theories survive quantization. This point is considered in section 8. We present a detailed analysis of the beta function in certain Witten type theories, and compute one-loop effects in Chern-Simons theory. (orig./HSI).
Wu, Ning
1998-01-01
In this paper, we will construct a gauge field model, in which the masses of gauge fields are non-zero and the local gauge symmetry is strictly preserved. A SU(N) gauge field model is discussed in details in this paper. In the limit $\\alpha \\longrightarrow 0$ or $\\alpha \\longrightarrow \\infty$, the gauge field model discussed in this paper will return to Yang-Mills gauge field model. This theory could be regarded as theoretical development of Yang-Mills gauge field theory.
Baden Fuller, A J
2014-01-01
Engineering Field Theory focuses on the applications of field theory in gravitation, electrostatics, magnetism, electric current flow, conductive heat transfer, fluid flow, and seepage.The manuscript first ponders on electric flux, electrical materials, and flux function. Discussions focus on field intensity at the surface of a conductor, force on a charged surface, atomic properties, doublet and uniform field, flux tube and flux line, line charge and line sink, field of a surface charge, field intensity, flux density, permittivity, and Coulomb's law. The text then takes a look at gravitation
From Classical to Quantum Shannon Theory
Wilde, Mark M
2011-01-01
The aim of this book is to develop "from the ground up" all of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
[The establishment, contributions, and final results of classical medical theories].
Wang, Tai
2013-01-01
In countries with ancient civilization of both Eastern world and Western world, after the accumulation of clinical experiences of "empirical medicine" to a sufficient amount; in accordance of their primitive philosophical thoughts, classical medical theories were established to play an important role in guiding the clinical practice of "empirical medicine". Because of the similarity of philosophical thoughts all over the ancient world, their medical theories were also very similar to each other. After the scientific evaluation and improvement, Greek classical medical theories were inherited, refined or abandoned, and then eventually finished their historical mission. Chinese classical medical theories also need the similar scientific identification and improvement for flowing into the authorized main stream of modern medical theory systems to continuously apply their guiding roles in clinical practice. Scholars would better consider the developmental principles of cultures and sciences with a historical viewpoint and an open mind to avoid making mistakes from haughty and prejudice. PMID:23596779
On the concept of Bell’s local causality in local classical and quantum theory
The aim of this paper is to implement Bell’s notion of local causality into a framework, called local physical theory. This framework, based on the axioms of algebraic field theory, is broad enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will arise as the classical case of our definition. Classifying local physical theories by whether they obey local primitive causality, a property rendering the dynamics of the theory causal, we then investigate what is needed for a local physical theory to be locally causal. Finally, comparing local causality with the common cause principles and relating both to the Bell inequalities we find a nice parallelism: Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively
Classical Coupled Mode Theory of Optomechanical Crystals
Khorasani, Sina
2016-01-01
Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an exact formulaion of coupled mode theory for interaction between elastic Bloch wave waves and photonic Bloch waves moving in a phonotonic waveguide. In general, an optical wavefront is strongly diffracted by an elastic wave in frequency and wavevector, and thus infinite modes with different frequencies and wavevectors appear. We discuss resonance and mode conversion conditions, and present a rigorous method to derive coupling rates and mode profiles. We also find a conservation law which rules over total optical power from interacting individual modes. Modifications of the theory to phonotonic cavities are also discussed. We present application examples including switch, frequency shifter, and reflector.
Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low utraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically, the idea is to integrate out the high frequency components of fields. This requires the choice of a 'blockspin', i.e. the specification af a low frequency field as a function of the fundamental fields. These blockspins will be fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspin in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels A from coarse to fine grid in addition to the averaging kernels C which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The special case of a 'lattice' with a single site (the constraint effective potential) is of particular interest. In a higgs model, the effective action reduces in this case to the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data. (orig.)
Antigravity and classical solutions of five-dimensional Kaluza-Klein theory
Classical solutions are exhibited of a graviton-graviphoton-graviscalar field theory which are antigravitating in the weak-field approximation. The theory itself is obtained by a Kaluza-Klein type reduction from five to four dimensions. The solutions are dyonic black holes with scalar charge. They share some similarities with the extreme Reissner-Nordstrom black holes of Einstein-Maxwell theory. (author)
Algebraic quantum field theory
The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)
Theory of Antisymmetric Tensor Fields
Dvoeglazov, V V
2003-01-01
It has long been claimed that the antisymmetric tensor field of the second rank is pure longitudinal after quantization. In my opinion, such a situation is quite unacceptable. I repeat the well-known procedure of the derivation of the set of Proca equations. It is shown that it can be written in various forms. Furthermore, on the basis of the Lagrangian formalism I calculate dynamical invariants (including the Pauli-Lubanski vector of relativistic spin for this field). Even at the classical level the Pauli-Lubanski vector can be equal to zero after applications of well-known constraints. The importance of the normalization is pointed out for the problem of the description of quantized fields of maximal spin 1. The correct quantization procedure permits us to propose a solution of this puzzle in the modern field theory. Finally, the discussion of the connection of the Ogievetskii-Polubarinov-Kalb-Ramond field and the electrodynamic gauge is presented.
Semi-classical theory of quiet lasers. I: Principles
Arnaud, J; Philippe, F; Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice
2006-01-01
When light originating from a laser diode driven by non-fluctuating electrical currents is incident on a photo-detector, the photo-current does not fluctuate much. Precisely, this means that the variance of the number of photo-electrons counted over a large time interval is much smaller that the average number of photo-electrons. At non-zero Fourier frequency $\\Omega$ the photo-current power spectrum is of the form $\\Omega^2/(1+\\Omega^2)$ and thus vanishes as $\\Omega\\to 0$, a conclusion equivalent to the one given above. The purpose of this paper is to show that results such as the one just cited may be derived from a (semi-classical) theory in which neither the optical field nor the electron wave-function are quantized. We first observe that almost any medium may be described by a circuit and distinguish (possibly non-linear) conservative elements such as pure capacitances, and conductances that represent the atom-field coupling. The theory rests on the non-relativistic approximation. Nyquist noise sources (...
Effective quantum field theories
Certain dimensional parameters play a crucial role in the understanding of weak and strong interactions based on SU(2) x U(1) and SU(3) symmetry group theories and of grand unified theories (GUT's) based on SU(5). These parameters are the confinement scale of quantum chromodynamics and the breaking scales of SU(2) x U(1) and SU(5). The concepts of effective quantum field theories and renormalisability are discussed with reference to the economics and ethics of research. (U.K.)
Grigorenko, Alexander Ya; Grigorenko, Yaroslav M; Vlaikov, Georgii G
2016-01-01
This volume focuses on the relevant general theory and presents some first applications, namely those based on classical shell theory. After a brief introduction, during which the history and state-of-the-art are discussed, the first chapter presents the mechanics of anisotropic heterogeneous shells, covering all relevant assumptions and the basic relations of 3D elasticity, classical and refined shell models. The second chapter examines the numerical techniques that are used, namely discrete orthogonalization, spline-collocation and Fourier series, while the third highlights applications based on classical theory, in particular, the stress-strain state of shallow shells, non-circular shells, shells of revolution, and free vibrations of conical shells. The book concludes with a summary and an outlook bridging the gap to the second volume.
Analog gravity from field theory normal modes?
Barcelo, Carlos; Liberati, Stefano; Visser, Matt
2001-01-01
We demonstrate that the emergence of a curved spacetime ``effective Lorentzian geometry'' is a common and generic result of linearizing a field theory around some non-trivial background. This investigation is motivated by considering the large number of ``analog models'' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (a field theoretic ...
A classical theory of continuous spin and hidden gauge invariance
We present a classical higher derivative point particle theory whose quantization gives Wigner's continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance
A classical theory of continuous spin and hidden gauge invariance
Zoller, D.
1991-01-01
We present a classical higher derivative point particle theory whose quantization gives Wigner's continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance.
A classical theory of continuous spin and hidden gauge invariance
Zoller, D.
1991-12-31
We present a classical higher derivative point particle theory whose quantization gives Wigner`s continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance.
Statistical mechanics and field theory
The first part applies field theory methods to statistical mechanics. In particular, statistical systems are related to fermionic-like field theories through a path integral representation. Such path integrals are over anticommuting variables. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. Chapter III solves by the methods of Chapters I and II a new model named the 128 pseudo-free vertex model. Chapter IV shows that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Chapter V addresses the most important problem in strong interaction physics: quark confinement. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks
Resonances and adiabatic invariance in classical and quantum scattering theory
Jain, S R
2004-01-01
We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal resonance-width and classical friction has been established with a classically deterministic quantity, the stability exponent of an adiabatically perturbed periodic orbit. This relation can be employed to estimate the rate of energy dissipation in finite quantum systems.
Petrov, Alexey A
2016-01-01
This book is a broad-based text intended to help the growing student body interested in topics such as gravitational effective theories, supersymmetric effective theories, applications of effective theory techniques to problems in condensed matter physics (superconductivity) and quantum chromodynamics (such as soft-collinear effective theory). It begins with a review of the use of symmetries to identify the relevant degrees of freedom in a problem, and then presents a variety of methods that can be used to solve physical problems. A detailed discussion of canonical examples of effective field theories with increasing complexity is then conducted. Special cases such as supersymmetry and lattice EFT are discussed, as well as recently-found applications to problems in gravitation and cosmology. An appendix includes various factoids from group theory and other topics that are used throughout the text, in an attempt to make the book self-contained.
Wentzel, Gregor
2003-01-01
A prominent figure in twentieth-century physics, Gregor Wentzel made major contributions to the development of quantum field theory, first in Europe and later at the University of Chicago. His Quantum Theory of Fields offers a knowledgeable view of the original literature of elementary quantum mechanics and helps make these works accessible to interested readers.An introductory volume rather than an all-inclusive account, the text opens with an examination of general principles, without specification of the field equations of the Lagrange function. The following chapters deal with particular
Field Theory of Gravitation: Desire and Reality
Baryshev, Yurij V.
1999-01-01
A retrospective analysis of the field theory of gravitation, describing gravitational field in the same way as other fields of matter in the flat space-time, is done. The field approach could be called "quantum gravidynamics" to distinguish it from the "geometrodynamics" or general relativity. The basic propositions and main conclusions of the field approach are discussed with reference to classical works of Birkhoff, Moshinsky, Thirring, Kalman, Feynman, Weinberg, Deser. In the case of weak ...
Homotopy Classification of Bosonic String Field Theory
Muenster, Korbinian; Sachs, Ivo
2012-01-01
We prove the decomposition theorem for the loop homotopy algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the op...
Field-theory methods in coagulation theory
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 = (n1, n2, ..., ng, ...), where ng is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional Ψ for the probability W(Q, t). The time evolution of Ψ is described by an equation that is similar to the Schrödinger 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.
This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks
On a Gauge Invariant Quantum Formulation for Non-gauge Classical Theory
I.L. Buchbinder; Pershin, V. D.; Toder, G. B.
1996-01-01
We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon...
Revision of the classical nucleation theory for supersaturated solutions
Borisenko, Alexander
2015-01-01
During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface and, therefore, alters the entire nucleation kinetics. Unless quite obvious, this effect has been ignored in the classical nucleation theory. To illustrate the results of this new approach, for the case of homogeneous nucleation, we calculate the total solubility (including the contribution from heterophase fluctuations) and the nucleation rate as functions of two parameters of the model and compare these results to the classical ones. One can conclude that discrepancies with the classical nucleation theory are great in the diffusion-limited regime, when the bulk diffusion mobility of solute atoms is small compared to the interfacial one, while in the opposite inter...
Gurau, Razvan
2009-01-01
Group field theories are higher dimensional generalizations of matrix models. Their Feynman graphs are fat and in addition to vertices, edges and faces, they also contain higher dimensional cells, called bubbles. In this paper, we propose a new, fermionic Group Field Theory, posessing a color symmetry, and take the first steps in a systematic study of the topological properties of its graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of this theory are well defined and readily identified. We prove that this graphs are combinatorial cellular complexes. We define and study the cellular homology of this graphs. Furthermore we define a homotopy transformation appropriate to this graphs. Finally, the amplitude of the Feynman graphs is shown to be related to the fundamental group of the cellular complex.
Zeidler, Eberhard
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...
Extende conformal field theories
Taormina, A. (Chicago Univ., IL (USA). Enrico Fermi Inst.)
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c{ge}1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification. (orig.).
Extended conformal field theories
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
We describe the construction of a class of cubic gauge-invariant actions for superstring field theory, and the gauge-fixing of one representative. Fermion string fields are taken in the -1/2-picture and boson string fields in the 0-picture, which makes a picture-changing insertion carrying picture number -2 necessary. The construction of all such operators is outlined. We discuss the gauge b1 + b-1 = 0, in which the action formally linearizes. Nontrivial scattering amplitudes are obtained by approaching this gauge as a limit. 20 refs
Theory of Optimal Currency Zones: from Classics until Today
Pinchuk Anastasiya K.
2013-12-01
Full Text Available The article analyses evolution of the theory of optimal currency zones (OCZ, starting from its classical provisions until moder developments. Based on the critical analysis of classical criteria of OCZ, the article develops a scheme of selection of the currency mode by the Robert Mundell theory. It considers achievements of the alternative OCZ theory, the main provisions of which are shown schematically in the form of illustrations of evolution of the theory of optimal currency zones. In the result of analysis of classical criteria of optimal currency zones and generalisation of developments of the new OCZ theory, the article develops a universal algorithm of identification of optimal conditions for an efficient currency zone. Using this algorithm allows identification of a system of quantitative indicators of expediency of regional joining the OCZ, on the basis of which one can build an economic model of an optimal currency zone, which reflects the degree of readiness of any country to join or develop the OCZ. Development of this model is necessary for many countries that face the need to select the currency integration. This model is of special importance for Ukraine, for which it is important to select the course of external integration, since various directions of foreign policy significantly influence efficiency of the domestic economic policy in the country.
Classical Bianchi Type I Cosmology in K-Essence Theory
2014-01-01
We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid ( p=γρ ) modeling the usual matter content and with cosmological constant Λ . Classical exact solutions for any γ≠1 and Λ=0 are found in closed form, whereas solutions for Λ≠0 are found for particular values in the barotropic parameter. We present the possible isotropization of the cosmological model Bianchi I using the ratio ...
THE NEW CLASSICAL THEORY AND THE REAL BUSINESS CYCLE MODEL
Oana Simona HUDEA (CARAMAN
2014-11-01
Full Text Available The present paper aims at describing some key elements of the new classical theory-related model, namely the Real Business Cycle, mainly describing the economy from the perspective of a perfectly competitive market, characterised by price, wage and interest rate flexibility. The rendered impulse-response functions, that help us in revealing the capacity of the model variables to return to their steady state under the impact of a structural shock, be it technology or monetary policy oriented, give points to the neutrality of the monetary entity decisions, therefore confirming the well-known classical dichotomy existing between the nominal and the real factors of the economy.
Holographic effective field theories
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
Holographic Effective Field Theories
Martucci, Luca
2016-01-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
Kim, S; Yee, H U; Kim, Seok; Lee, Ki-Myeong; Yee, Ho-Ung
2006-01-01
To a domain wall or string object, Noether charge and topological spatial objects can be attracted, forming a composite BPS (Bogomolny-Prasad-Sommerfield) object. We consider two field theories and derive a new BPS bound on composite linear solitons involving multiple charges. Among the BPS objects `supertubes' appear when the wall or string tension is canceled by the bound energy, and could take an arbitrary closed curve. In our theories, supertubes manifest as Chern-Simons solitons, dyonic instantons, charged semi-local vortices, and dyonic instantons on vortex flux sheet.
Quantum Field Theory in a Semiotic Perspective
Günter Dosch, Hans; Sieroka, Norman
2005-01-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...
Classic Grounded Theory to Analyse Secondary Data: Reality and Reflections
Lorraine Andrews
2012-06-01
Full Text Available This paper draws on the experiences of two researchers and discusses how they conducted a secondary data analysis using classic grounded theory. The aim of the primary study was to explore first-time parents’ postnatal educational needs. A subset of the data from the primary study (eight transcripts from interviews with fathers was used for the secondary data analysis. The objectives of the secondary data analysis were to identify the challenges of using classic grounded theory with secondary data and to explore whether the re-analysis of primary data using a different methodology would yield a different outcome. Through the process of re-analysis a tentative theory emerged on ‘developing competency as a father’. Challenges encountered during this re-analysis included the small dataset, the pre-framed data, and limited ability for theoretical sampling. This re-analysis proved to be a very useful learning tool for author 1(LA, who was a novice with classic grounded theory.
We have given several pieces of evidence that perturbation theory manages to reproduce various salient features of the conjectured exact S-matrices of ATFT. At present, we do not see how to use perturbation theory to provide an efficient description of the quantum field theory; an alternative formulation may well be required in order to find a proper understanding of the conjectured S-matrices and other features such as the mass-renormalization and the Clebsch-Gordan property. Certainly, the knowledge from other approaches, for example, the Quantum Group approach to imaginary coupling ATFT, investigations of the Bethe-Salpeter equations for the bound states in ATFT and the algebraic Bethe ansatz method advocated for many years by Faddeev and others would be helpful in the search for such a re-formulation. (J.P.N.)
Alvarez-Gaumé, Luís
1996-01-01
Quantum Field Theory provides the most fundamental language known to express the fundamental laws of Nature. It is the consequence of trying to describe physical phenomena within the conceptual framework of Quantum Mechanics and Special Relativity. The aim of these lectures will be to present a number of concepts and methods in the subject which many of us find difficult to understand. They may include (depending on time) : the need to introduce quantum fields, the realization of symmetries, the renormalization group, non-perturbative phenomena, infrared divergences and jets, etc. Some familiarity with the rudiments of Feynman diagrams and relativistic quantum mechanics will be appreciated.
The traversable wormhole with classical scalar fields
Kim, S. -W; Kim, S. P.
1999-01-01
We study the Lorentzian static traversable wormholes coupled to quadratic scalar fields. We also obtain the solutions of the scalar fields and matters in the wormhole background and find that the minimal size of the wormhole should be quantized under the appropriate boundary conditions for the positive non-minimal massive scalar field.
PREFACE: Particles and Fields: Classical and Quantum
Asorey, M.; Clemente-Gallardo, J.; Marmo, G.
2007-07-01
This volume contains some of the contributions to the Conference Particles and Fields: Classical and Quantum, which was held at Jaca (Spain) in September 2006 to honour George Sudarshan on his 75th birthday. Former and current students, associates and friends came to Jaca to share a few wonderful days with George and his family and to present some contributions of their present work as influenced by George's impressive achievements. This book summarizes those scientific contributions which are presented as a modest homage to the master, collaborator and friend. At the social ceremonies various speakers were able to recall instances of his life-long activity in India, the United States and Europe, adding colourful remarks on the friendly and intense atmosphere which surrounded those collaborations, some of which continued for several decades. This meeting would not have been possible without the financial support of several institutions. We are deeply indebted to Universidad de Zaragoza, Ministerio de Educación y Ciencia de España (CICYT), Departamento de Ciencia, Tecnología y Universidad del Gobierno de Aragón, Universitá di Napoli 'Federico II' and Istituto Nazionale di Fisica Nucleare. Finally, we would like to thank the participants, and particularly George's family, for their contribution to the wonderful atmosphere achieved during the Conference. We would like also to acknowledge the authors of the papers collected in the present volume, the members of the Scientific Committee for their guidance and support and the referees for their generous work. M Asorey, J Clemente-Gallardo and G Marmo The Local Organizing Committee George Sudarshan International Advisory Committee A. Ashtekhar (Pennsylvania State University, USA) L. J. Boya (Universidad de Zaragoza, Spain) I. Cirac (Max Planck Institute, Garching, Germany) G. F. Dell Antonio (Universitá di Roma La Sapienza, Italy) A. Galindo (Universidad Complutense de Madrid, Spain) S. L. Glashow (Boston University
Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
Hanany, Amihay
2016-01-01
We approach the topic of Classical group nilpotent orbits from the perspective of their moduli spaces, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKahler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for ...
Classical nucleation theory for cavitation processes in water
Němec, Tomáš; Maršík, František
Antalya : HEFAT, 2010 - (Meyer, J.), s. 2035-2040 ISBN 978-1-86854-818-7. [International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2010) /7./. Antalya (TR), 19.07.2010-21.07.2010] R&D Projects: GA ČR(CZ) GA106/08/0557; GA ČR GAP101/10/1819 Institutional research plan: CEZ:AV0Z20760514 Keywords : cavitation * classical nucleation theory * water Subject RIV: BJ - Thermodynamics
THE NEW CLASSICAL THEORY AND THE REAL BUSINESS CYCLE MODEL
Oana Simona HUDEA (CARAMAN); Sorin George TOMA; Marin BURCEA
2014-01-01
The present paper aims at describing some key elements of the new classical theory-related model, namely the Real Business Cycle, mainly describing the economy from the perspective of a perfectly competitive market, characterised by price, wage and interest rate flexibility. The rendered impulse-response functions, that help us in revealing the capacity of the model variables to return to their steady state under the impact of a structural shock, be it technology or monetary policy oriented, ...
Local Energy Velocity of Classical Fields
Drozdov, I. V.; Stahlhofen, A. A.
2007-01-01
It is proposed to apply a recently developed concept of local wave velocities to the dynamical field characteristics, especially for the canonical field energy density. It is shown that local energy velocities can be derived from the lagrangian directly. The local velocities of zero- and first- order for energy propagation has been obtained for special cases of scalar and vector fields. Some important special cases of these results are discussed.
A New Fuzzy Set Theory Satisfying All Classical Set Formulas
Qing-Shi Gao; Xiao-Yu Gao; Yue Hu
2009-01-01
A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set system, in which all fuzzy sets must be "non-uniform inclusive" to each other, then it forms a family of sub-systems, the Z-fuzzy set family. It can be proved that the Z0-fuzzy set system, one of Z-fuzzy set systems, is equivalent to Zadeh's fuzzy set system. Analysis shows that 1) Zadeh's fuzzy set system defines the relations A = B and A ∈B between two fuzzy sets A and B as "Vu e U,(u A E (u)=μB(U))" and "Au ∈ U, (μA(U) ≤μB(μ))" respectively is inappropriate, because it makes all fuzzy sets be "non-uniformly inclusive"; 2) it is also inappropriate to define two fuzzy sets' union and intersection operations as the max and rain of their grades of membership, because this prevents fuzzy set's ability to correctly reflect different kinds of fuzzy phenomenon in the natural world. Then it has to work around the problem by invent unnatural functions that are hard to understand, such as augmenting max and min for union and intersection to min{a + b, 1} and max{a + b - 1, 0}, but these functions are incorrect on inclusive case. If both pairs of definitions are used together, not only are they unnatural, but also they are still unable to cover all possible set relationships in the natural world; and 3) it is incorrect to define the set complement as 1 -μA(μ), because it can be proved that set complement cannot exist in Zadeh's fuzzy set, and it causes confusion in logic and thinking. And it is seriously mistaken to believe that logics of fuzzy sets necessarily go against classical and normal thinking, logic, and conception. The C-fuzzy set theory proposed in this paper overcomes all of the above errors and shortcomings, and more reasonably reflects fuzzy phenomenon in the natural world. It satisfies all relations, formulas, and operations of the
Geometric aspects in extended approach of equilibrium classical fluctuation theory
Velazquez, L.
2011-11-01
Previously, an extended approach of equilibrium classical fluctuation theory was developed compatible with the existence of anomalous response functions, e.g. states with negative heat capacities. Now, the geometric aspects associated with this new framework are analyzed. The analysis starts from the so-called reparametrization invariance: a special symmetry of distribution functions dp (I|θ) employed in classical equilibrium statistical mechanics that allows us to express the thermo-statistical relations in the same mathematical appearance in different coordinate representations. The existence of reparametrization invariance can be related to three different geometric frameworks: (1) a non-Riemannian formulation for classical fluctuation theory based on the concept of reparametrization dualities; (2) a Riemannian formulation defined on the manifold {P} of control parameters θ, where the main theorems of inference theory appear as dual counterparts of general fluctuation theorems, and Boltzmann-Gibbs distributions ωBG(I|θ) = exp(-θiIi)/Z(θ) admit a geometric generalization; and finally, (3) a Riemannian formulation defined on the manifold {M}_{\\theta } of macroscopic observables I, which appears as a counterpart approach of inference geometry.
The facets of relativistic quantum field theory
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
From quantum gravity to quantum field theory via noncommutative geometry
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction, which encodes the kinematics of quantum gravity, we construct semi-classical states which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The emergent interaction involves flux tubes of the gravitational field. In the additional limit, where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. (paper)
Development of a unified viscoplasticity constitutive model based on classical plasticity theory
GUAN Ping; LIU ChangChun; L(U) HeXiang
2009-01-01
The traditional unified viscoplasticity constitutive model can be only applied to metal materials. The study of the unified constitutive theory for metal materials has discovered the correlation between the classical plasticity theory and the unified viscoplasticity constitutive model, thus leading to the con-cepts of the classic plastic potential and yield surface in the unified constitutive model. Moreover, this research has given the continuous expression of the classical plastic multiplier and presented the corresponding constructive method, which extends its physical significance and lays down a good foundation for the application of the unified constitutive theory to the material analysis in more fields.This paper also introduces the unified constitutive model for metal materials and geo-materials. The numerical simulation indicates that the construction should be both reasonable and practical.
Development of a unified viscoplasticity constitutive model based on classical plasticity theory
无
2009-01-01
The traditional unified viscoplasticity constitutive model can be only applied to metal materials.The study of the unified constitutive theory for metal materials has discovered the correlation between the classical plasticity theory and the unified viscoplasticity constitutive model,thus leading to the con-cepts of the classic plastic potential and yield surface in the unified constitutive model.Moreover,this research has given the continuous expression of the classical plastic multiplier and presented the corresponding constructive method,which extends its physical significance and lays down a good foundation for the application of the unified constitutive theory to the material analysis in more fields.This paper also introduces the unified constitutive model for metal materials and geo-materials.The numerical simulation indicates that the construction should be both reasonable and practical.
A New Conformal Theory of Semi-Classical Quantum General Relativity
Suhendro I.
2007-10-01
Full Text Available We consider a new four-dimensional formulation of semi-classical quantum general relativity in which the classical space-time manifold, whose intrinsic geometric properties give rise to the effects of gravitation, is allowed to evolve microscopically by means of a conformal function which is assumed to depend on some quantum mechanical wave function. As a result, the theory presented here produces a unified field theory of gravitation and (microscopic electromagnetism in a somewhat simple, effective manner. In the process, it is seen that electromagnetism is actually an emergent quantum field originating in some kind of stochastic smooth extension (evolution of the gravitational field in the general theory of relativity.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
For a quantum field coupled to a classical background gsub(μnu)-field we propose a recursive technique which relates the diagonal matrix element to its value at t=-infinity. We then employ the lowest non-trivial order to renormalize the semi-classical theory of gravity. The existence of two important classes of solutions of the linearized theory is briefly discussed. (author)
Higgs Effective Field Theories
2016-01-01
The main focus of this meeting is to present new theoretical advancements related to effective field theories, evaluate the impact of initial results from the LHC Run2, and discuss proposals for data interpretation/presentation during Run2. A crucial role of the meeting is to bring together theorists from different backgrounds and with different viewpoints and to extend bridges towards the experimental community. To this end, we would like to achieve a good balance between senior and junior speakers, enhancing the visibility of younger scientists while keeping some overview talks.