Franklin, Joel
2017-01-01
Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...
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...
Introduction to classical and quantum field theory
International Nuclear Information System (INIS)
Ng, Tai-Kai
2009-01-01
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.)
Special relativity and classical field theory
Susskind, Leonard
2017-01-01
Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.
Quantum scattering from classical field theory
International Nuclear Information System (INIS)
Gould, T.M.; Poppitz, E.R.
1995-01-01
We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial-value conditions. The initial-value conditions are such as to make the solution of the classical field equations amenable to numerical methods. We propose a practical procedure for computing classical solutions which contribute to high energy two-particle scattering amplitudes. We consider in this regard the implications of a recent numerical simulation in classical SU(2) Yang-Mills theory for multiparticle scattering in quantum gauge theories and speculate on its generalization to electroweak theory. We also generalize our results to the case of complex trajectories and discuss the prospects for finding a solution to the resulting complex boundary value problem, which would allow the application of our method to any wave packet to coherent state transition. Finally, we discuss the relevance of these results to the issues of baryon number violation and multiparticle scattering at high energies. ((orig.))
Classical trajectories and quantum field theory
International Nuclear Information System (INIS)
Vitiello, Giuseppe; Istituto Nazionale di Fisica Nucleare, Salerno
2005-01-01
The density matrix and the Wigner function formalism requires the doubling of the degrees of freedom in quantum mechanics (QM) and quantum field theory (QFT). The doubled degrees of freedom play the role of the thermal bath or environment degrees of freedom and are entangled with the system degrees of freedom. They also account for quantum noise in the fluctuating random forces in the system-environment coupling. The algebraic structure of QFT turns out to be the one of the deformed Hopf algebra. In such a frame, the trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations turn out to be classical trajectories and, under convenient conditions, they may exhibit properties typical of classical chaotic trajectories in nonlinear dynamics. The quantum Brownian motion and the two-slit experiment in QM are discussed in connection with the doubling of the degrees of freedom. (author)
Gauge bridges in classical field theory
International Nuclear Information System (INIS)
Jakobs, S.
2009-03-01
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.)
Classical Solutions in Quantum Field Theory
International Nuclear Information System (INIS)
Mann, Robert
2013-01-01
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
Lectures on classical and quantum theory of fields
Arodz, Henryk
2017-01-01
This textbook 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. 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
Energy Technology Data Exchange (ETDEWEB)
Arodz, Henryk; Hadasz, Leszek [Jagiellonian Univ., Krakow (Poland). Inst. Physics
2010-07-01
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. (orig.)
Lectures on classical and quantum theory of fields
International Nuclear Information System (INIS)
Arodz, Henryk; Hadasz, Leszek
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. (orig.)
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.
Quantum fermions and quantum field theory from classical statistics
International Nuclear Information System (INIS)
Wetterich, Christof
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 Schrödinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.
Constrained variational calculus for higher order classical field theories
Energy Technology Data Exchange (ETDEWEB)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)
2010-11-12
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Constrained variational calculus for higher order classical field theories
International Nuclear Information System (INIS)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn
2010-01-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Asymptotic Conservation Laws in Classical Field Theory
International Nuclear Information System (INIS)
Anderson, I.M.; Torre, C.G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society
Generalized force in classical field theory. [Euler-Lagrange equations
Energy Technology Data Exchange (ETDEWEB)
Krause, J [Universidad Central de Venezuela, Caracas
1976-02-01
The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.
The spin-statistics connection in classical field theory
International Nuclear Information System (INIS)
Morgan, J A
2006-01-01
The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group corresponding to general causal fields is reviewed. The connection is obtained by imposing local commutativity on the fields and exploiting the parity operation to exchange spatial coordinates in the scalar product of classical field evaluated at one spatial location with the same field evaluated at a distinct location. The spin-statistics connection for irreducible canonical realizations of the Poincare group of spin j is obtained in the form: classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2j even and fundamental Poisson antibracket relations for 2j odd
Classical electromagnetic field theory in the presence of magnetic sources
Chen, Wen-Jun; Li, Kang; Naón, Carlos
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.
Second quantization of classical nonlinear relativistic field theory. Pt. 2
International Nuclear Information System (INIS)
Balaban, T.
1976-01-01
The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de
Classically integrable boundary conditions for affine Toda field theories
International Nuclear Information System (INIS)
Bowcock, P.; Corrigan, E.; Dorey, P.E.; Rietdijk, R.H.
1995-01-01
Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory. (orig.)
On the mathematical theory of classical fields and general relativity
Klainerman, S
1993-01-01
From the perspective of an analyst, like myself, the General Theory of Relativity provides an extrordinary rich and vastly virgin territory. It is the aim of my lecture to provide, ﬁrst, an account of those aspects of the theory which attract me most and second a perspective of what has been accomplished so far in that respect. In trying to state our main objectives it helps to view General Relativity in the broader context of Classical Field Theory. EinsteiniVacuum equations, or shortly E—V, is already sufﬁciently complicated. I will thus restrict my attention to them.
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
Motion of small bodies in classical field theory
International Nuclear Information System (INIS)
Gralla, Samuel E.
2010-01-01
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.
Remarks on the classical limit of quantum field theories
International Nuclear Information System (INIS)
Eckmann, J.P.
1977-01-01
Recently, there has been an increasing interest in computing quantum mechanical corrections to solutions of classical field equations. In this note, proceeding in the opposite way, theorems about the classical limit of relativistic quantum field models are summarized. These results are a byproduct of the so called 'constructive' approach to quantum field theory. Section 1 deals with generalities; in Section 2 the situation where no phase transitions occur is discussed in the limit h→0; and in Section 3 one result in the case where such a transition occurs is reformulated (Glimm et al). The validity of the loop expansion is discussed. It seems however that the tools to show the rigorous validity of soliton calculations are not yet prepared. (Auth.)
Local gauge invariant Lagrangeans in classical field theories
International Nuclear Information System (INIS)
Grigore, D.R.
1982-07-01
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)
Gauge-fields and integrated quantum-classical theory
International Nuclear Information System (INIS)
Stapp, H.P.
1986-01-01
Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs
Quasiperiodical orbits in the scalar classical lambdaphi4 field theory
International Nuclear Information System (INIS)
Belova, T.I.; Kudryavtsev, A.E.
1985-01-01
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
An application of information theory to stochastic classical gravitational fields
Angulo, J.; Angulo, J. C.; Angulo, J. M.
2018-06-01
The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.
On the construction of classical superstring field theories
Energy Technology Data Exchange (ETDEWEB)
Konopka, Sebastian Johann Hermann
2016-07-01
This thesis describes the construction of classical superstring field theories based on the small Hilbert space. First we describe the traditional construction of perturbative superstring theory as an integral over the supermoduli space of type II world sheets. The geometry of supermoduli space dictates many algebraic properties of the string field theory action. In particular it allows for an algebraisation of the construction problem for classical superstring field theories in terms of homotopy algebras. Next, we solve the construction problem for open superstrings based on Witten's star product. The construction is recursive and involves a choice of homotopy operator for the zero mode of the η-ghost. It turns out that the solution can be extended to the Neveu-Schwarz subsectors of all superstring field theories. The recursive construction involves a hierarchy of string products at various picture deficits. The construction is not entirely natural, but it is argued that different choices give rise to solutions related by a field redefinition. Due to the presence of odd gluing parameters for Ramond states the extension to full superstring field theory is non-trivial. Instead, we construct gauge-invariant equations of motion for all superstring field theories. The realisation of spacetime supersymmetry in the open string sector is highly non-trivial and is described explicitly for the solution based on Witten's star product. After a field redefinition the non-polynomial equations of motion and the small Hilbert space constraint become polynomial. This polynomial system is shown to be supersymmetric. Quite interestingly, the supersymmetry algebra closes only up to gauge transformations. This indicates that only the physical phase space realizes N=1 supersymmetry. Apart from the algebraic constraints dictated by the geometry of supermoduli space the equations of motion or action should reproduce the traditional string S-matrix. The S-matrix of a field
Geometry of Lagrangian first-order classical field theories
International Nuclear Information System (INIS)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N.
1996-01-01
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.)
Geometry of Lagrangian first-order classical field theories
Energy Technology Data Exchange (ETDEWEB)
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.)
Principles of physics from quantum field theory to classical mechanics
Jun, Ni
2014-01-01
This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics. Readership: This is an advanced gradua...
Classical nucleation theory in the phase-field crystal model.
Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas
2018-04-01
A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.
Classical nucleation theory in the phase-field crystal model
Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas
2018-04-01
A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.
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...
On covariant Poisson brackets in classical field theory
International Nuclear Information System (INIS)
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 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
Energy Technology Data Exchange (ETDEWEB)
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.
New solutions of a nonlinear classical field theory
International Nuclear Information System (INIS)
Marques, G.C.; Ventura, I.
1975-01-01
New solutions of a relativistic, classical, field theoretical model having logarithmic nonlinearities are obtained. Some of these solutions correspond to field not bounded in time but having finite energy and charge. There are no bounded solutions (bound states and resonances in particular) if the charge exceeds a certain value. This effect is due to the existance of a 'charge barrier' in this field theoretical model. All calculations are performed in a number of spatial dimensions [pt
Anyons as spin particles: from classical mechanics to field theory
Plyushchay, Mikhail S.
1995-01-01
(2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of linear differential field equations.
Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.
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Scheck, Florian
2018-04-01
Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook 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's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's 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's 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 with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.
Classical field theory on electrodynamics, non-abelian gauge theories and gravitation
Scheck, Florian
2018-01-01
Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook 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's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's 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's 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...
Prequantum classical statistical field theory: background field as a source of everything?
International Nuclear Information System (INIS)
Khrennikov, Andrei
2011-01-01
Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's 'double solution' approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special 'prequantum fields': the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the 'photonic field' (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of 'vacuum fluctuations') might play the role of a source of such pulses, i.e., the source of everything.
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Thierry-Mieg, J.
1985-01-01
This paper discusses 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
International Nuclear Information System (INIS)
Thierry-Mieg, J.
1985-01-01
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...
Lower Bound on the Energy Density in Classical and Quantum Field Theories.
Wall, Aron C
2017-04-14
A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant energy condition. In a quantum field theory, there instead exists a quantum energy condition, i.e., a lower bound on the energy density that depends on information-theoretic quantities. Some extensions to higher dimensions are briefly discussed.
k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations
Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
2012-06-01
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.
k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations
International Nuclear Information System (INIS)
Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
2012-01-01
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.
Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in φ4-Theory
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Finster, Felix; Tolksdorf, Juergen
2012-01-01
Solutions of the classical φ 4 -theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a ''classical measurement process'' in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.
Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory
Finster, Felix; Tolksdorf, Jürgen
2012-05-01
Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.
Tensor algebra over Hilbert space: Field theory in classical phase space
International Nuclear Information System (INIS)
Matos Neto, A.; Vianna, J.D.M.
1984-01-01
It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt
Classical open-string field theory: A∞-algebra, renormalization group and boundary states
International Nuclear Information System (INIS)
Nakatsu, Toshio
2002-01-01
We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. Classical open-string field theory in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of A ∞ -algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles
On the classical origins of yangian symmetry in integrable field theory
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MacKay, N.J.
1992-01-01
We show that Drinfeld's yangian algebra, studied recently as the algebra of conserved charges in certain two-dimensional integrable quantum field theories, is also present in the classical theory as a Poisson-Hopf algebra, and exhibit explicitly the Serre relations, coproduct and antipode. (orig.)
International Nuclear Information System (INIS)
Brandt, R.A.; Neri, F.; Zwanziger, D.
1979-01-01
We establish the Lorentz invariance of the quantum field theory of electric and magnetic charge. This is a priori implausible because the theory is the second-quantized version of a classical field theory which is inconsistent if the minimally coupled charged fields are smooth functions. For our proof we express the generating functional for the gauge-invariant Green's functions of quantum electrodynamics: with or without magnetic charge: as a path integral over the trajectories of classical charged point particles. The electric-electric and electric-magnetic interactions contribute factors exp(JDJ) and exp(JD'K), where J and K are the electric and magnetic currents of classical point particles and D is the usual photon propagator. The propagator D' involves the Dirac string but exp(JD'K) depends on it only through a topological integer linking string and classical particle trajectories. The charge quantization condition e/sub i/g/sub j/ - g/sub i/e/sub j/ = integer then suffices to make the gauge-invariant Green's functions string independent. By implication our formulation shows that if the Green's functions of quantum electrodynamics are expressed as usual as functional integrals over classical charged fields, the smooth field configurations have measure zero and all the support of the Feynman measure lies on the trajectories of classical point particles
Microcanonical simulations in classical and quantum field theory
International Nuclear Information System (INIS)
Olson, D.P.
1988-01-01
In the first part of this thesis, a stochastic adaptation of the microcanonical simulation method is applied to the numerical simulation of the Su-Schrieffer-Heeger Hamiltonian for polyacetylene, a one-dimensional polymer were fermion-boson interactions play a dominant role in the dynamics of the system. The pure microcanonical simulation method fails in the marginally ergodic case and a stochastic adaptation, the hybrid microcanonical method, is employed to resolve problems with ergodicity. The hybrid method is shown to be an efficient method for higher dimensional fermionic quantum systems. In the second part of this thesis, a numerical simulation of the evolution of a network of global cosmic strings is an expanding Robertson-Walker universe is carried out. The system is quenched through an order-disorder phase transition and the nature of the string distribution is examined. While the string distribution observed at the phase transition is in good agreement with earlier estimates, the simulation reveals that the dynamics of the strings are suppressed by interactions with the Goldstone field. The network decays by topological annihilation and no spatial correlations are observed at any point in the simulation
An analogue of the Heisenberg uncertainty relation in prequantum classical field theory
Energy Technology Data Exchange (ETDEWEB)
Khrennikov, Andrei, E-mail: Andrei.Khrennikov@vxu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, University of Vaexjoe, Vaexjoe (Sweden) and Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)
2010-02-01
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.
An analogue of the Heisenberg uncertainty relation in prequantum classical field theory
International Nuclear Information System (INIS)
Khrennikov, Andrei
2010-01-01
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.
International Nuclear Information System (INIS)
Remler, E.A.
1977-01-01
A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed
Geometrical phases from global gauge invariance of nonlinear classical field theories
International Nuclear Information System (INIS)
Garrison, J.C.; Chiao, R.Y.
1988-01-01
We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics
Classical field theory in the space of reference frames. [Space-time manifold, action principle
Energy Technology Data Exchange (ETDEWEB)
Toller, M [Dipartimento di Matematica e Fisica, Libera Universita, Trento (Italy)
1978-03-11
The formalism of classical field theory is generalized by replacing the space-time manifold M by the ten-dimensional manifold S of all the local reference frames. The geometry of the manifold S is determined by ten vector fields corresponding to ten operationally defined infinitesimal transformations of the reference frames. The action principle is written in terms of a differential 4-form in the space S (the Lagrangian form). Densities and currents are represented by differential 3-forms in S. The field equations and the connection between symmetries and conservation laws (Noether's theorem) are derived from the action principle. Einstein's theory of gravitation and Maxwell's theory of electromagnetism are reformulated in this language. The general formalism can also be used to formulate theories in which charge, energy and momentum cannot be localized in space-time and even theories in which a space-time manifold cannot be defined exactly in any useful way.
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 ...
Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory
International Nuclear Information System (INIS)
Pons, Josep M.
2011-01-01
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.
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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 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 φ 4 theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society
International Nuclear Information System (INIS)
Scheck, Florian
2010-01-01
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. [de
Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Directory of Open Access Journals (Sweden)
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.
Relativistic and nonrelativistic classical field theory on fivedimensional space-time
International Nuclear Information System (INIS)
Kunzle, H.P.; Duval, C.
1985-07-01
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
A New Semi-Symmetric Uniﬁed Field Theory of the Classical Fields of Gravity and Electromagnetism
Directory of Open Access Journals (Sweden)
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 ...
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.
Field transformations and the classical equation of motion in chiral perturbation theory
International Nuclear Information System (INIS)
Scherer, S.; Fearing, H.W.
1995-01-01
The construction of effective Lagrangians commonly involves the application of the ''classical equation of motion'' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at O(p 6 ). The use of the ''classical equation of motion'' is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond O(p 4 ). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss
Gauge bridges in classical field theory; Eichbruecken in der klassischen Feldtheorie
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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.)
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...
Classical tokamak transport theory
International Nuclear Information System (INIS)
Nocentini, Aldo
1982-01-01
A qualitative treatment of the classical transport theory of a magnetically confined, toroidal, axisymmetric, two-species plasma is presented. The 'weakly collisional' ('banana' and 'plateau') and 'collision dominated' ('Pfirsch-Schlueter' and 'highly collisional') regimes, as well as the Ware effect are discussed. The method used to evaluate the diffusion coffieicnts of particles and heat in the weakly collisional regime is based on stochastic argument, that requires an analysis of the characteristic collision frequencies and lengths for particles moving in a tokamak-like magnetic field. The same method is used to evaluate the Ware effect. In the collision dominated regime on the other hand, the particle and heat fluxes across the magnetic field lines are dominated by macroscopic effects so that, although it is possible to present them as diffusion (in fact, the fluxes turn out to be proportional to the density and temperature gradients), a macroscopic treatment is more appropriate. Hence, fluid equations are used to inveatigate the collision dominated regime, to which particular attention is devoted, having been shown relatively recently that it is more complicated than the usual Pfirsch-Schlueter regime. The whole analysis presented here is qualitative, aiming to point out the relevant physical mechanisms involved in the various regimes more than to develop a rigorous mathematical derivation of the diffusion coefficients, for which appropriate references are given. (author)
International Nuclear Information System (INIS)
Wu Ning; Zhang Dahua
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.
Nonlinear classical theory of electromagnetism
International Nuclear Information System (INIS)
Pisello, D.
1977-01-01
A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere. (author)
Non-Gaussian statistics, classical field theory, and realizable Langevin models
International Nuclear Information System (INIS)
Krommes, J.A.
1995-11-01
The direct-interaction approximation (DIA) to the fourth-order statistic Z ∼ left-angle λψ 2 ) 2 right-angle, where λ is a specified operator and ψ is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z DIA already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (''spurious vertices'') is described. It is shown how to derive an improved representation, that realizes cumulants through O(ψ 4 ), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z DIA M to Z DIA is derived. Both Z DIA and Z DIA M incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example
The classical field limit of scattering theory for non-relativistic many-boson systems. Pt. 1
International Nuclear Information System (INIS)
Ginibre, J.
1979-01-01
We study the classical field limit of non-relativistic many-boson theories in space dimension n >= 3. When h → 0, the correlation functions, which are the averages of products of bounded functions of field operators at different times taken in suitable states, converge to the corresponding functions of the appropriate solutions of the classical field equation, and the quantum fluctuations, are described by the equation obtained by linearizing the field equation around the classical solution. These properties were proved by Hepp for suitably regular potentials and in finite time intervals. Using a general theory of existence of global solutions and a general scattering theory for the clasical equation, we extend these results in two directions: (1) we consider more singular potentials, (2) more imortant, we prove that for dispersive classical solutions, the h → 0 limit is uniform in time in an appropriate representation of the field operators. As a consequence we obtain the convergence of suitable matrix elements of the wave operators and, if asymptotic completeness holds, of the S-matrix. (orig.) [de
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of
Energy Technology Data Exchange (ETDEWEB)
Múnera, Héctor A., E-mail: hmunera@hotmail.com [Centro Internacional de Física (CIF), Apartado Aéreo 4948, Bogotá, Colombia, South America (Colombia); Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America (Colombia)
2016-07-07
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.
Energy Technology Data Exchange (ETDEWEB)
Scheck, Florian [Mainz Univ. (Germany). Inst. fuer Physik
2017-09-01
The following topics are dealt with: Maxwell's equations together with their symmetry and covariance, the Maxwell theory as classical field theory, simple applications of Maxwell's theory, local gauge theories, classical field theory of gravitation. (HSI)
Quantization in the neighborhood of a classical solution in the theory of a Fermi field
International Nuclear Information System (INIS)
Sveshnikov, K.A.
1988-01-01
The quantization of a Fermi-Bose field system in the neighborhood of a classical solution of the equations of motion that contains both bosonic and spinor components is considered. The latter is regarded as an absolutely anticommuting (Grassmann) component of a fermion field. On account of the transport of the fermion number, such an object mixes the fermionic and bosonic and fermionic and antifermionic degrees of freedom already at the level of the single-particle states (in the approximately of quadratic forms). Explicit expressions are obtained for the operator of the S matrix, which describes such transport processes, and the total Hamiltonian and total fermion charge of the system in this approximation
International Nuclear Information System (INIS)
Bruneton, Jean-Philippe
2007-01-01
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
From classical to quantum fields
Baulieu, Laurent; Sénéor, Roland
2017-01-01
Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a re...
Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program
Manin, Yuri I.
Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].
Point-particle effective field theory I: classical renormalization and the inverse-square potential
Energy Technology Data Exchange (ETDEWEB)
Burgess, C.P.; Hayman, Peter [Physics & Astronomy, McMaster University,Hamilton, ON, L8S 4M1 (Canada); Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada); Williams, M. [Instituut voor Theoretische Fysica, KU Leuven,Celestijnenlaan 200D, B-3001 Leuven (Belgium); Zalavári, László [Physics & Astronomy, McMaster University,Hamilton, ON, L8S 4M1 (Canada); Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)
2017-04-19
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential’s singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original problem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.
Currents and the energy-momentum tensor in classical field theory: a fresh look at an old problem
International Nuclear Information System (INIS)
Forger, Michael; Roemer, Hartmann
2004-01-01
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of 'improving' the expressions provided by the canonical Noether procedure is addressed and given an adequate geometric framework. The main new ingredient is the explicit formulation of a principle of 'ultralocality' with respect to the symmetry generators, which is shown to fix the ambiguity inherent in the procedure of improvement and guide it towards a unique answer: when combined with the appropriate splitting of the fields into sectors, it leads to the well-known expressions for the current as the variational derivative of the matter field Lagrangian with respect to the gauge field and for the energy-momentum tensor as the variational derivative of the matter field Lagrangian with respect to the metric tensor. In the second case, the procedure is shown to work even when the matter field Lagrangian depends explicitly on the curvature, thus establishing the correct relation between scale invariance, in the form of local Weyl invariance 'on shell', and tracelessness of the energy-momentum tensor, required for a consistent definition of the concept of a conformal field theory
Consistent classical supergravity theories
International Nuclear Information System (INIS)
Muller, M.
1989-01-01
This book offers a presentation of both conformal and Poincare supergravity. The consistent four-dimensional supergravity theories are classified. The formulae needed for further modelling are included
Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton
2017-03-28
Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.
Natarajan, P N
2017-01-01
This book presents results about certain summability methods, such as the Abel method, the Norlund method, the Weighted mean method, the Euler method and the Natarajan method, which have not appeared in many standard books. It proves a few results on the Cauchy multiplication of certain summable series and some product theorems. It also proves a number of Steinhaus type theorems. In addition, it introduces a new definition of convergence of a double sequence and double series and proves the Silverman-Toeplitz theorem for four-dimensional infinite matrices, as well as Schur's and Steinhaus theorems for four-dimensional infinite matrices. The Norlund method, the Weighted mean method and the Natarajan method for double sequences are also discussed in the context of the new definition. Divided into six chapters, the book supplements the material already discussed in G.H.Hardy's Divergent Series. It appeals to young researchers and experienced mathematicians who wish to explore new areas in Summability Theory.
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.
International Nuclear Information System (INIS)
Konstantinovich, A.V.; Melnychuk, S.V.; Konstantinovich, I.A.
2002-01-01
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)
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.
Lagrangian formulation of classical BMT-theory
International Nuclear Information System (INIS)
Pupasov-Maksimov, Andrey; Deriglazov, Alexei; Guzman, Walberto
2013-01-01
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)
International Nuclear Information System (INIS)
Oeien, A.H.
1977-06-01
Sets of lower order and higher order kinetic and macroscopic equations are developed for a plasma where collisions are important but electrons and ions are allowed to have different temperatures when transports, due to gradients and fields, set in. Solving the lower order kinetic equations and taking appropriate velocity moments we show that usual classical transports emerge. From the higher order kinetic equations special notice is taken of some new correction terms to the classical transports. These corrections are linear in gradients and fields, some of which are found in a two-temperature state only. (Auth.)
Introduction to gauge field theory
International Nuclear Information System (INIS)
Bailin, David; Love, Alexander
1986-01-01
The book is intended as an introduction to gauge field theory for the postgraduate student of theoretical particle physics. The topics discussed in the book include: path integrals, classical and quantum field theory, scattering amplitudes, feynman rules, renormalisation, gauge field theories, spontaneous symmetry breaking, grand unified theory, and field theories at finite temperature. (UK)
On the Foundational Equations of the Classical Theory of ...
Indian Academy of Sciences (India)
IAS Admin
... Equations of the Classical. Theory of Electrodynamics ... most cherished notions of the Maxwell{Lorentz theory .... dia in the presence of the fields, in which case a self- consistent ..... could benefit from further experimental verification, we.
International Nuclear Information System (INIS)
Souza, Manoelito M. de
1997-01-01
We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Nonlocal continuum field theories
2002-01-01
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...
International Nuclear Information System (INIS)
Drechsler, W.; Havas, P.; Rosenblum, A.
1984-01-01
In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g
International Nuclear Information System (INIS)
Douglas, Michael R.; Nekrasov, Nikita A.
2001-01-01
This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level
1999-11-08
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.
Perturbation theory via Feynman diagrams in classical mechanics
Penco, R.; Mauro, D.
2006-01-01
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.
A survey on classical minimal surface theory
Meeks, William H
2012-01-01
Meeks and Pérez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in three-dimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many currently active leading mathematicians, thus making contact with much of the most important results in the field. Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject. This book includes an updated tour through some of the recent advances in the theory, such as Colding-Minicozzi theory, minimal laminations, the ordering theorem for the space of ends, conformal structure of minimal surfaces, minimal annular ends with infinite total curvature, the embedded Calabi-Yau problem, local pictures on the scale of curvature and t...
Gravitation in the 'quasi-classical' theory
International Nuclear Information System (INIS)
Wignall, J.W.G.; Zangari, M.
1990-01-01
The 'quasi-classical' picture of particles as extendend periodic disturbances in a classical nonlinear field, previously shown to imply all the equations of Maxwell electrodynamics with very little formal input, is here applied to the other known long-range force, gravitation. It is shown that the picture's absolute interpretation of inertial mass and four-potential as measures of the local spacing between equal-phase hypersurfaces, together with the empirically established proportionality of gravitational 'charge' to inertial mass, leads naturally to the gravitational red-shift formula, and it thus provides a physical basis for the spacetime curvature that is the central idea of Einstein's general theory of relativity. 16 refs., 1 fig
Energy Technology Data Exchange (ETDEWEB)
Kumar, A.; Choudhury, S. [Electronics and Communication Engineering, Sikkim Manipal Institute of Technology, Majitar, East Sikkim 737 132 (India); Saha, S. [Electronics and Communication Engineering, Mallabhum Institute of Technology College Campus, Brajaradhanagar, P.O. Gosaipur, P.S. Bishnupur, District - Bankura 722 122 (India); Pahari, S. [Administration Department, Jadavpur University, Kolkata 700 032 (India); De, D. [Department of Computer Science Engineering, West Bengal University of Technology, BF 142, Sector 1, Kolkatta 700 064, West Bengal (India); Bhattacharya, S. [Nano Scale Device Research Laboratory, Center for Electronics Design and Technology, Indian Institute of Science, Bangalore 560 012 (India); Ghatak, K.P., E-mail: kamakhyaghatak@yahoo.co.i [Department of Electronic Science, University Calcutta, 92 Acharyya Prafulla Chandra Road, Kolkata 700 009 (India)
2010-01-01
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 CdGeAs{sub 2}, 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.
International Nuclear Information System (INIS)
Leite Lopes, J.
1981-01-01
The book is intended to explain, in an elementary way, the basic notions and principles of gauge theories. Attention is centred on the Salem-Weinberg model of electro-weak interactions, as well as neutrino-lepton scattering and the parton model. Classical field theory, electromagnetic, Yang-Mills and gravitational gauge fields, weak interactions, Higgs mechanism and the SU(5) model of grand unification are also discussed. (U.K.)
International Nuclear Information System (INIS)
Boyer, T.H.
1975-01-01
The theory of classical electrodynamics with classical electromagnetic zero-point radiation is outlined here under the title random electrodynamics. The work represents a reanalysis of the bounds of validity of classical electron theory which should sharpen the understanding of the connections and distinctions between classical and quantum theories. The new theory of random electrodynamics is a classical electron theory involving Newton's equations for particle motion due to the Lorentz force, and Maxwell's equations for the electromagnetic fields with point particles as sources. However, the theory departs from the classical electron theory of Lorentz in that it adopts a new boundary condition on Maxwell's equations. It is assumed that the homogeneous boundary condition involves random classical electromagnetic radiation with a Lorentz-invariant spectrum, classical electromagnetic zero-point radiation. The implications of random electrodynamics for atomic structure, atomic spectra, and particle-interference effects are discussed on an order-of-magnitude or heuristic level. Some detailed mathematical connections and some merely heuristic connections are noted between random electrodynamics and quantum theory. (U.S.)
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)
2016-06-06
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.
Matricial theory in classical photoelasticity
International Nuclear Information System (INIS)
Apostol, D.
1980-01-01
The matrix calculus in classical photoelasticity is used. Transfer functions for different polariscope arrangements are calculated. Linear polariscopes, circular polariscopes, double-exposure method to obtain isochromatics and Tardy and Senarmont method of measuring fractional relative retardations are analysed using coherency matrix formalism. (author)
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
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...
Generalizability Theory and Classical Test Theory
Brennan, Robert L.
2011-01-01
Broadly conceived, reliability involves quantifying the consistencies and inconsistencies in observed scores. Generalizability theory, or G theory, is particularly well suited to addressing such matters in that it enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over…
Theory of interacting quantum fields
International Nuclear Information System (INIS)
Rebenko, Alexei L.
2012-01-01
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 20 th 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.
Classical and non-classical effective medium theories: New perspectives
Energy Technology Data Exchange (ETDEWEB)
Tsukerman, Igor, E-mail: igor@uakron.edu
2017-05-18
Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.
Classical and non-classical effective medium theories: New perspectives
International Nuclear Information System (INIS)
Tsukerman, Igor
2017-01-01
Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.
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
Studies in quantum field theory
International Nuclear Information System (INIS)
Bender, C.M.; Mandula, J.E.; Shrauner, J.E.
1982-01-01
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
Microcanonical quantum field theory
International Nuclear Information System (INIS)
Strominger, A.
1983-01-01
Euclidean quantum field theory is equivalent to the equilibrium statistical mechanics of classical fields in 4+1 dimensions at temperature h. It is well known in statistical mechanics that the theory of systems at fixed temperature is embedded within the more general and fundamental theory of systems at fixed energy. We therefore develop, in precise analogy, a fixed action (macrocanonical) formulation of quantum field theory. For the case of ordinary renormalizable field theories, we show (with one exception) that the microcanonical is entirely equivalent to the canonical formulation. That is, for some particular fixed value of the total action, the Green's functions of the microcanonical theory are equal, in the bulk limit, to those of the canonical theory. The microcanonical perturbation expansion is developed in some detail for lambdaphi 4 . The particular value of the action for which the two formulations are equivalent can be calculated to all orders in perturbation theory. We prove, using Lehmann's Theorem, that this value is one-half Planck unit per degree of freedom, if fermionic degrees of freedom are counted negatively. This is the 4+1 dimensional analog of the equipartition theorem. The one exception to this is supersymmetric theories. A microcanonical formulation exists if and only if supersymmetry is broken. In statistical mechanics and in field theory there are systems for which the canonical description is pathological, but the microcanonical is not. An example of such a field theory is found in one dimension. A semiclassical expansion of the microcanonical theory is well defined, while an expansion of the canonical theory is hoplessly divergent
Classical diffusion: theory and simulation codes
International Nuclear Information System (INIS)
Grad, H.; Hu, P.N.
1978-03-01
A survey is given of the development of classical diffusion theory which arose from the observation of Grad and Hogan that the Pfirsch-Schluter and Neoclassical theories are very special and frequently inapplicable because they require that plasma mass flow be treated as transport rather than as a state variable of the plasma. The subsequent theory, efficient numerical algorithms, and results of various operating codes are described
Classical field approach to quantum weak measurements.
Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco
2014-03-21
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.
Lorente, M.
2003-01-01
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of any dimension invariant and apply these transformations to field equations.
Topics in quantum field theory
International Nuclear Information System (INIS)
Svaiter, N.F.
2006-11-01
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
The significance of classical structures in quantum theories
International Nuclear Information System (INIS)
Lowe, M.J.
1978-09-01
The implications for the quantum theory of the presence of non-linear classical solutions of the equations of motion are investigated in various model systems under the headings: (1) Canonical quantisation of the soliton in lambdaphi 4 theory in two dimensions. (2) Bound for soliton masses in two dimensional field theories. (3) The canonical quantisation of a soliton like solution in the non-linear schrodinger equation. (4) The significance of the instanton classical solution in a quantum mechanical system. (U.K.)
Classical geometry from the quantum Liouville theory
Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin
2005-09-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl
2005-09-26
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
International Nuclear Information System (INIS)
Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin
2005-01-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
Hilbert space; Koopman–von Neumann theory; classical electrodynamics. PACS No. 03.50. ... The paper is divided into four sections. Section 2 .... construction of Sudarshan is to be contrasted with that of Koopman and von Neumann. ..... ture from KvN and [16] in this formulation is to define new momentum and coordinate.
Classical solutions in lattice gauge theories
International Nuclear Information System (INIS)
Mitrjushkin, V.K.
1996-08-01
The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed. (orig.)
Classical quantum theory of wobbling modes
International Nuclear Information System (INIS)
Onishi, Naoki
1986-01-01
Wobbling modes are studied extensively in terms of time-dependent variational theory. Quantum states and their energies are determined by the Bohr-Sommerfeld rule of classical quantization. Numerical calculations are performed for states of 166 Er with vertical strokejvertical stroke=30-40 (h/2π). (orig.)
"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).
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
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin
2016-05-01
In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.
Classical limit for scalar fields at high temperature
International Nuclear Information System (INIS)
Buchmueller, W.; Jakovac, A.
1998-01-01
We study real-time correlation functions in scalar quantum field theories at temperature T=1/β. We show that the behaviour of soft, long-wavelength modes is determined by classical statistical field theory. The loss of quantum coherence is due to interactions with the soft modes of the thermal bath. The soft modes are separated from the hard modes by an infrared cutoff Λ<<1/(ℎβ). Integrating out the hard modes yields an effective theory for the soft modes. The infrared cutoff Λ controls corrections to the classical limit which are O(ℎβΛ). As an application, the plasmon damping rate is calculated. (orig.)
The classical theory of fields
Landau, Lev Davidovich
1975-01-01
Translated from the 6th Russian edition, this latest edition contains seven new sections with chapters on General Relativity, Gravitational Waves and Relativistic Cosmology, where Professor Lifshitz's interests lay. The text of the 3rd English edition has been thoroughly revised and additional problems inserted
Optimal search behavior and classic foraging theory
International Nuclear Information System (INIS)
Bartumeus, F; Catalan, J
2009-01-01
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.
Theories of Matter, Space and Time; Classical theories
Evans, N.; King, S. F.
2017-12-01
This book and its sequel ('Theories of Matter Space and Time: Quantum Theories') are taken from third and fourth year undergraduate Physics courses at Southampton University, UK. The aim of both books is to move beyond the initial courses in classical mechanics, special relativity, electromagnetism, and quantum theory to more sophisticated views of these subjects and their interdependence. The goal is to guide undergraduates through some of the trickier areas of theoretical physics with concise analysis while revealing the key elegance of each subject. The first chapter introduces the key areas of the principle of least action, an alternative treatment of Newtownian dynamics, that provides new understanding of conservation laws. In particular, it shows how the formalism evolved from Fermat's principle of least time in optics. The second introduces special relativity leading quickly to the need and form of four-vectors. It develops four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment; then returns to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again, it then returns to the action principle to formulate minimal substitution for an electrically charged particle.
Towards chaos criterion in quantum field theory
Kuvshinov, V. I.; Kuzmin, A. V.
2002-01-01
Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.
Emergence of classical theories from quantum mechanics
International Nuclear Information System (INIS)
Hájícek, P
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 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.
Nonrelativistic Schroedinger equation in quasi-classical theory
International Nuclear Information System (INIS)
Wignall, J.W.G.
1987-01-01
The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field chi(x,t), interacting with each other via nonlinearity in the equation of motion for chi. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from chi a configuration-space wave function Psi(x 1 , X 2 , t), and that the theory requires that Psi satisfy the two-particle Schroedinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schroedinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials
Pisutha-Arnond, N; Chan, V W L; Iyer, M; Gavini, V; Thornton, K
2013-01-01
We introduce a new approach to represent a two-body direct correlation function (DCF) in order to alleviate the computational demand of classical density functional theory (CDFT) and enhance the predictive capability of the phase-field crystal (PFC) method. The approach utilizes a rational function fit (RFF) to approximate the two-body DCF in Fourier space. We use the RFF to show that short-wavelength contributions of the two-body DCF play an important role in determining the thermodynamic properties of materials. We further show that using the RFF to empirically parametrize the two-body DCF allows us to obtain the thermodynamic properties of solids and liquids that agree with the results of CDFT simulations with the full two-body DCF without incurring significant computational costs. In addition, the RFF can also be used to improve the representation of the two-body DCF in the PFC method. Last, the RFF allows for a real-space reformulation of the CDFT and PFC method, which enables descriptions of nonperiodic systems and the use of nonuniform and adaptive grids.
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.
Semiclassical methods in field theories
International Nuclear Information System (INIS)
Ventura, I.
1978-10-01
A new scheme is proposed for semi-classical quantization in field theory - the expansion about the charge (EAC) - which is developed within the canonical formalism. This method is suitable for quantizing theories that are invariant under global gauge transformations. It is used in the treatment of the non relativistic logarithmic theory that was proposed by Bialynicki-Birula and Mycielski - a theory we can formulate in any number of spatial dimensions. The non linear Schroedinger equation is also quantized by means of the EAC. The classical logarithmic theories - both, the non relativistic and the relativistic one - are studied in detail. It is shown that the Bohr-Sommerfeld quantization rule(BSQR) in field theory is, in many cases, equivalent to charge quantization. This rule is then applied to the massive Thirring Model and the logarithmic theories. The BSQR can be see as a simplified and non local version of the EAC [pt
[Taxonomic theory for non-classical systematics].
Pavlinov, I Ia
2012-01-01
Outlined briefly are basic principles of construing general taxonomic theory for biological systematics considered in the context of non-classical scientific paradigm. The necessity of such kind of theory is substantiated, and some key points of its elaboration are exposed: its interpretation as a framework concept for the partial taxonomic theories in various schools of systematics; elaboration of idea of cognitive situation including three interrelated components, namely subject, object, and epistemic ones; its construing as a content-wisely interpreted quasi-axiomatics, with strong structuring of its conceptual space including demarcation between axioms and inferring rules; its construing as a "conceptual pyramid" of concepts of various levels of generality; inclusion of a basic model into definition of the taxonomic system (classification) regulating its content. Two problems are indicated as fundamental: definition of taxonomic diversity as a subject domain for the systematics as a whole; definition of onto-epistemological status of taxonomic system (classification) in general and of taxa in particular.
Characterization of particle states in relativistic classical quantum theory
International Nuclear Information System (INIS)
Horwitz, L.P.; Rabin, Y.
1977-02-01
Classical and quantum relativistic mechanics are studied. The notion of a ''particle'' is defined in the classical case and the interpretation of mechanics in space-time is clarified. These notions are carried over to the quantum theory, as much as possible. The relation between the results of Feyman's path integral approach and the theory of Horwitz and Piron is discussed. The ''particle'' interpretation is shown to imply an asymptotic condition for scattering. A general method of constructing the dynamical mass spectrum of composite ''particle'' states is discussed. An interference experiment is proposed to affirm the interpretation and applicability of Stueckelberg type wave functions for actual physical phenomena. Some discussion of the relation of this relativistic quantum theory to Feynman's approach to quantum field theory is also given
Differential formalism aspects of the gauge classical theories
International Nuclear Information System (INIS)
Stedile, E.
1982-01-01
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.) [pt
Relativistic classical limit of quantum theory
International Nuclear Information System (INIS)
Shin, G.R.; Rafelski, J.
1993-01-01
We study the classical limit of the equal-time relativistic quantum transport theory. We discuss in qualitative terms the need to fold first the Wigner function with a coarse-graining function. Only then does the singularity at ℎ→0 seem to be manageable. In the limit ℎ→0, we obtain the relativistic Vlasov equations for the particle and the antiparticle sector of the Fock space. Similarly, we address the evolution equations of the spin and the magnetic-moment density
String theory or field theory?
International Nuclear Information System (INIS)
Marshakov, A.V.
2002-01-01
The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments, which are our concern in this review [ru
Geometric function theory: a modern view of a classical subject
International Nuclear Information System (INIS)
Crowdy, Darren
2008-01-01
Geometric function theory is a classical subject. Yet it continues to find new applications in an ever-growing variety of areas such as modern mathematical physics, more traditional fields of physics such as fluid dynamics, nonlinear integrable systems theory and the theory of partial differential equations. This paper surveys, with a view to modern applications, open problems and challenges in this subject. Here we advocate an approach based on the use of the Schottky–Klein prime function within a Schottky model of compact Riemann surfaces. (open problem)
Classical and quantum mechanics of non-abelian gauge fields
International Nuclear Information System (INIS)
Savvidy, G.K.
1984-01-01
Classical and quantum mechanics of non-abelian gauge fields are investigated both with and without spontaneous symmetry breaking. The fundamental subsystem (FS) of Yang-Mills classical mechanics (YMCM) is considered. It is shown to be a Kolmogorov K-system, and hence to have strong statistical properties. Integrable systems are also found, to which in terms of KAM theory Yang-Mills-Higgs classical mechanics (YMHCM) is close. Quantum-mechanical properties of the YM system and their relation to the problem of confinement are discussed. (orig.)
The evolving Planck mass in classically scale-invariant theories
Energy Technology Data Exchange (ETDEWEB)
Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H. [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia)
2017-04-05
We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.
The evolving Planck mass in classically scale-invariant theories
Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H.
2017-04-01
We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.
On the consistency of classical and quantum supergravity theories
Energy Technology Data Exchange (ETDEWEB)
Hack, Thomas-Paul [II. Institute for Theoretical Physics, University of Hamburg (Germany); Makedonski, Mathias [Department of Mathematical Sciences, University of Copenhagen (Denmark); Schenkel, Alexander [Department of Stochastics, University of Wuppertal (Germany)
2012-07-01
It is known that pure N=1 supergravity in d=4 spacetime dimensions is consistent at a classical and quantum level, i.e. that in a particular gauge the field equations assume a hyperbolic form - ensuring causal propagation of the degrees of freedom - and that the associated canonical quantum field theory satisfies unitarity. It seems, however, that it is yet unclear whether these properties persist if one considers the more general and realistic case of N=1, d=4 supergravity theories including arbitrary matter fields. We partially clarify the issue by introducing novel hyperbolic gauges for the gravitino field and proving that they commute with the resulting equations of motion. Moreover, we review recent partial results on the unitarity of these general supergravity theories and suggest first steps towards a comprehensive unitarity proof.
International Nuclear Information System (INIS)
Galvao, C.A.P.; Mignaco, J.A.
1994-01-01
The classical electromagnetic theory is analysed which corresponds to the two-dimensional quantum electrodynamics with massless spinor fields (Schwinger model). The chiral anomaly is introduced as a currents property, which in the two-dimensional spinor fields are duality related. It is also shown that the resulting classical theory is consistent. (author). 5 refs
String theory or field theory?
International Nuclear Information System (INIS)
Marshakov, Andrei V
2002-01-01
The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments which are our concern in this review. (reviews of topical problems)
International Nuclear Information System (INIS)
Bergmann, P.G.
1980-01-01
A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion
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...
Field theories with subcanonical fields
International Nuclear Information System (INIS)
Bigi, I.I.Y.
1976-01-01
The properties of quantum field theories with spinor fields of dimension less than the canonical value of 3/2 are studied. As a starting point for the application of common perturbation theory we look for the linear version of these theories. A gange-interaction is introduced and with the aid of power counting the renormalizability of the theory is shown. It follows that in the case of a spinor-field with negative dimension renormalization can only be attained if the interaction has a further symmetry. By this symmetry the theory is determined in an unequivocal way. The gange-interaction introduced in the theory leads to a spontaneous breakdown of scale invariance whereby masses are produced. At the same time the spinor-field operators can now be separated in two orthogonal sections with opposite norm. It is proposed to use the section with negative (positive) norm to describe hadrons (leptons) respectively. (orig./WL) [de
Classical behavior of a scalar field in the inflationary universe
International Nuclear Information System (INIS)
Sasaki, Misao; Nambu, Yasusada; Nakao, Ken-ichi.
1987-09-01
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)
Covariant Noncommutative Field Theory
Energy Technology Data Exchange (ETDEWEB)
Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
Covariant Noncommutative Field Theory
International Nuclear Information System (INIS)
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-01-01
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
Pseudo-classical theory of Majorana-Weyl particle
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1996-01-01
A pseudo-classical theory of Weyl particle in the space-time dimensions D = 2 n is constructed. The canonical quantization of that pseudo-classical theory is carried out and it results in the theory of the D = 2 n dimensional Weyl particle in the Foldy-Wouthuysen representation. 28 refs
Representational Realism, Closed Theories and the Quantum to Classical Limit
de Ronde, Christian
In this chapter, we discuss the representational realist stance as a pluralistontic 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 superposition problem and the contextuality problem, which consider explicitly the conceptual representation of orthodox QM beyond the mere reference to mathematical structures and measurement outcomes. In the final part of the chapter, we revisit, from representational realist perspective, the quantum to classical limit and the orthodox claim that this inter-theoretic relation can be explained through the principle of decoherence.
International Nuclear Information System (INIS)
Prasad, R.
1975-01-01
Results of researches into Unified Field Theory over the past seven years are presented. The subject is dealt with in chapters entitled: the choice of affine connection, algebraic properties of the vector fields, field laws obtained from the affine connection based on the path integral method, application to quantum theory and cosmology, interpretation of physical theory in terms of geometry. (U.K.)
Effective quantum field theories
International Nuclear Information System (INIS)
Georgi, H.M.
1993-01-01
The most appropriate description of particle interactions in the language of quantum field theory depends on the energy at which the interactions are studied; the description is in terms of an ''effective field theory'' that contains explicit reference only to those particles that are actually important at the energy being studied. The various themes of the article are: local quantum field theory, quantum electrodynamics, new physics, dimensional parameters and renormalizability, socio-dynamics of particle theory, spontaneously broken gauge theories, scale dependence, grand unified and effective field theories. 2 figs
Classical and semi-classical solutions of the Yang--Mills theory
International Nuclear Information System (INIS)
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator
Antigravity and classical solutions of five-dimensional Kaluza-Klein theory
Energy Technology Data Exchange (ETDEWEB)
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.
Classical solutions of some field theoretic models
International Nuclear Information System (INIS)
Zakrzewski, W.J.
1982-01-01
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.)
Fundamental theories of waves and particles formulated without classical mass
Fry, J. L.; Musielak, Z. E.
2010-12-01
Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called 'wave mass', which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
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.
International Nuclear Information System (INIS)
Bonara, L.; Cotta-Ramusino, P.; Rinaldi, M.
1987-01-01
It is well-known that type I and heterotic superstring theories have a zero mass spectrum which correspond to the field content of N=1 supergravity theory coupled to supersymmetric Yang-Mills theory in 10-D. The authors study the field theory ''per se'', in the hope that simple consistency requirements will determine the theory completely once one knows the field content inherited from string theory. The simplest consistency requirements are: N=1 supersymmetry; and absence of chiral anomalies. This is what the authors discuss in this paper here leaving undetermined the question of the range of validity of the resulting field theory. As is known, a model of N=1 supergravity (SUGRA) coupled to supersymmetric Yang-Mills (SYM) theory was known in the form given by Chapline and Manton. The coupling of SUGRA to SYM was determined by the definition of the ''field strength'' 3-form H in this paper
International Nuclear Information System (INIS)
Ryder, L.H.
1985-01-01
This introduction to the ideas and techniques of quantum field theory presents the material as simply as possible and is designed for graduate research students. After a brief survey of particle physics, the quantum theory of scalar and spinor fields and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a bridge survey of ''topological'' objects in field theory and assumes a knowledge of quantum mechanics and special relativity
International Nuclear Information System (INIS)
Kaku, M.
1987-01-01
In this article, the authors summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. They also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group they call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). The geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory
Algebraic conformal field theory
International Nuclear Information System (INIS)
Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1991-11-01
Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs
International Nuclear Information System (INIS)
Khoury, Justin
2013-01-01
Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated by chameleons therefore depends sensitively on their environment, which makes for a rich phenomenology. In this paper, we review two recent results on chameleon phenomenology. The first result a pair of no-go theorems limiting the cosmological impact of chameleons and their generalizations: (i) the range of the chameleon force at cosmological density today can be at most ∼Mpc; (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time. These theorems imply that chameleons have negligible effect on the linear growth of structure, and cannot account for the observed cosmic acceleration except as some form of dark energy. The second result pertains to the quantum stability of chameleon theories. We show how requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound of m −3 ) 1/3 eV for gravitational strength coupling, whereas fifth force experiments place a lower bound of m > 0.0042 eV. An improvement of less than a factor of 2 in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well-controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. (paper)
Supersymmetric gauge theories with classical groups via M theory fivebrane
International Nuclear Information System (INIS)
Terashima, S.
1998-01-01
We study the moduli space of vacua of four-dimensional N=1 and N=2 supersymmetric gauge theories with the gauge groups Sp(2N c ), SO(2N c ) and SO(2N c +1) using the M theory fivebrane. Higgs branches of the N=2 supersymmetric gauge theories are interpreted in terms of the M theory fivebrane and the type IIA s-rule is realized in it. In particular, we construct the fivebrane configuration which corresponds to a special Higgs branch root. This root is analogous to the baryonic branch root in the SU(N c ) theory which remains as a vacuum after the adjoint mass perturbation to break N=2 to N=1. Furthermore, we obtain the monopole condensations and the meson vacuum expectation values in the confining phase of N=1 supersymmetric gauge theories using the fivebrane technique. These are in complete agreement with the field theory results for the vacua in the phase with a single confined photon. (orig.)
A Tulczyjew triple for classical fields
International Nuclear Information System (INIS)
Grabowska, Katarzyna
2012-01-01
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. (paper)
Large N field theories, string theory and gravity
Energy Technology Data Exchange (ETDEWEB)
Maldacena, J [Lyman Laboratory of Physics, Harvard University, Cambridge (United States)
2002-05-15
We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/ M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions. These lecture notes are based on the Review written by O. Aharony, S. Gubser, J. Maldacena, H. Ooguri and Y. Oz. (author)
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.
International Nuclear Information System (INIS)
Eloranta, E.
2003-11-01
The geophysical field theory includes the basic principles of electromagnetism, continuum mechanics, and potential theory upon which the computational modelling of geophysical phenomena is based on. Vector analysis is the main mathematical tool in the field analyses. Electrostatics, stationary electric current, magnetostatics, and electrodynamics form a central part of electromagnetism in geophysical field theory. Potential theory concerns especially gravity, but also electrostatics and magnetostatics. Solid state mechanics and fluid mechanics are central parts in continuum mechanics. Also the theories of elastic waves and rock mechanics belong to geophysical solid state mechanics. The theories of geohydrology and mass transport form one central field theory in geophysical fluid mechanics. Also heat transfer is included in continuum mechanics. (orig.)
Field theory and the Standard Model
Energy Technology Data Exchange (ETDEWEB)
Dudas, E [Orsay, LPT (France)
2014-07-01
This brief introduction to Quantum Field Theory and the Standard Model contains the basic building blocks of perturbation theory in quantum field theory, an elementary introduction to gauge theories and the basic classical and quantum 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 constructions.
Classical field configurations and infrared slavery
Swanson, Mark S.
1987-09-01
The problem of determining the energy of two spinor particles interacting through massless-particle exchange is analyzed using the path-integral method. A form for the long-range interaction energy is obtained by analyzing an abridged vertex derived from the parent theory. This abridged vertex describes the radiation of zero-momentum particles by pointlike sources. A path-integral formalism for calculating the energy of the radiation field associated with this abridged vertex is developed and applications are made to determine the energy necessary for adiabatic separation of two sources in quantum electrodynamics and for an SU(2) Yang-Mills theory. The latter theory is shown to be consistent with confinement via infrared slavery.
[Studies in quantum field theory
International Nuclear Information System (INIS)
1990-01-01
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
Superspace conformal field theory
Energy Technology Data Exchange (ETDEWEB)
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
International Nuclear Information System (INIS)
Quella, Thomas
2013-07-01
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.
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)
Introduction to quantum field theory
Chang, Shau-Jin
1990-01-01
This book presents in a short volume the basics of quantum field theory and many body physics. The first part introduces the perturbative techniques without sophisticated apparatus and applies them to numerous problems including quantum electrodynamics (renormalization), Fermi and Bose gases, the Brueckner theory of nuclear system, liquid Helium and classical systems with noise. The material is clear, illustrative and the important points are stressed to help the reader get the understanding of what is crucial without overwhelming him with unnecessary detours or comments. The material in the s
Baal, Pierre Van
2014-01-01
""… a pleasant novelty that manages the impossible: a full course in field theory from a derivation of the Dirac equation to the standard electroweak theory in less than 200 pages. Moreover, the final chapter consists of a careful selection of assorted problems, which are original and either anticipate or detail some of the topics discussed in the bulk of the chapters. Instead of building a treatise out of a collection of lecture notes, the author took the complementary approach and constructed a course out of a number of well-known and classic treatises. The result is fresh and useful. … the
Hyperfunction quantum field theory
International Nuclear Information System (INIS)
Nagamachi, S.; Mugibayashi, N.
1976-01-01
The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not contain C infinitely functios with compact support. In spite of this defect the support concept of H-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory. (orig.) [de
Sadovskii, Michael V
2013-01-01
This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.
Vertex operator algebras and conformal field theory
International Nuclear Information System (INIS)
Huang, Y.Z.
1992-01-01
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics
International Nuclear Information System (INIS)
Hohm, Olaf; Zwiebach, Barton
2017-01-01
We review and develop the general properties of L_∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L_∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L_∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L_∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L_∞ algebra for the interacting theory. The analysis suggests that L_∞ algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
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
Classical limit of a quantum particle in an external Yang-Mills field
International Nuclear Information System (INIS)
Moschella, U.
1989-01-01
It is studied the classical limit of a quantum particle in an external non-abelian gauge field. It is shown that the unitary group describing the quantum fluctuations around any classic phase orbit has a classical limit when h tends to zero under very general conditions on the potentials. It is also proved the self-adjointness of the Hamilton's operator of the quantum theory for a large class of potentials. Some applications of the theory are finally exposed
Toward finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1986-01-01
The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)
Nonequilibrium quantum field theories
International Nuclear Information System (INIS)
Niemi, A.J.
1988-01-01
Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena. (orig.)
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…
Supersymmetric gauge field theories
International Nuclear Information System (INIS)
Slavnov, A.A.
1976-01-01
The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models
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...
Mandl, Franz
2010-01-01
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic
WORKSHOP: Thermal field theory
Energy Technology Data Exchange (ETDEWEB)
Anon.
1989-04-15
The early history of the Universe is a crucial testing ground for theories of elementary particles. Speculative ideas about the constituents of matter and their interactions are reinforced if they are consistent with what we suppose happened near the beginning of time and discarded if they are not. The cosmological consequences of these theories are usually deduced using a general statistical approach called thermal field theory. Thus, 75 physicists from thirteen countries met in Cleveland, Ohio, last October for the first 'Workshop on Thermal Field Theories and their Applications'.
Experimental assessment of unvalidated assumptions in classical plasticity theory.
Energy Technology Data Exchange (ETDEWEB)
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.
Classical confining solutions of a tensor gauge theory incorporating colour
International Nuclear Information System (INIS)
Salam, A.; Strathdee, J.
1977-04-01
A mass-modified Einstein-Weyl gauge theory of colour carrying spin-two mesons is formulated. A classical solution is exhibited for the case of internal SU(2) symmetry which may confine quarks in colour singlets
A superstring field theory for supergravity
Reid-Edwards, R. A.; Riccombeni, D. A.
2017-09-01
A covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.
The semi classical laser theory and some applications of laser
International Nuclear Information System (INIS)
Abdalla, Abbaker Ali
1995-04-01
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)
International Nuclear Information System (INIS)
Mack, G.; Kalkreuter, T.; Palma, G.; Speh, M.
1992-05-01
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.)
Algebraic quantum field theory
International Nuclear Information System (INIS)
Foroutan, A.
1996-12-01
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)
Effective quantum field theories
International Nuclear Information System (INIS)
Georgi, H.M.
1989-01-01
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.)
International Nuclear Information System (INIS)
Strominger, A.
1987-01-01
A gauge invariant cubic action describing bosonic closed string field theory is constructed. The gauge symmetries include local spacetime diffeomorphisms. The conventional closed string spectrum and trilinear couplings are reproduced after spontaneous symmetry breaking. The action S is constructed from the usual ''open string'' field of ghost number minus one half. It is given by the associator of the string field product which is non-vanishing because of associativity anomalies. S does not describe open string propagation because open string states associate and can thereby be shifted away. A field theory of closed and open strings can be obtained by adding to S the cubic open string action. (orig.)
Mean fields and self consistent normal ordering of lattice spin and gauge field theories
International Nuclear Information System (INIS)
Ruehl, W.
1986-01-01
Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)
Chance, determinism and the classical theory of probability.
Vasudevan, Anubav
2018-02-01
This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning. Copyright © 2017 Elsevier Ltd. All rights reserved.
Functional methods underlying classical mechanics, relativity and quantum theory
International Nuclear Information System (INIS)
Kryukov, A
2013-01-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is ''made'' of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.
Quaternionic quantum field theory
International Nuclear Information System (INIS)
Adler, S.L.
1986-01-01
In this paper the author describes a new kind of quantum mechanics or quantum field theory based on quaternions. Quaternionic quantum mechanics has a Schrodinger equation, a Dirac transformation theory, and a functional integral. Quaternionic quantum mechanics does not seem to have (except in the complex quantum mechanics specialization): A correspondence principle, and beyond this a commuting tensor product, asymptotic states, an S-matrix, a canonical formalism, coherent states or a Euclidean continuation. A new kind of quantum mechanics exists. There are many interesting formal questions to study, which should enable one to decide whether quaternionic quantum field theory is relevant for particle physics
International Nuclear Information System (INIS)
Pokorski, S.
1987-01-01
Quantum field theory forms the present theoretical framework for the understanding of the fundamental interactions of particle physics. This book examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. The author discusses field-theoretical techniques and encourages the reader to perform many of the calculations presented. This book includes a brief introduction to perturbation theory, the renormalization programme, and the use of the renormalization group equation. Several topics of current research interest are covered, including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry
Finite temperature field theory
Das, Ashok
1997-01-01
This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are al
Interpolating string field theories
International Nuclear Information System (INIS)
Zwiebach, B.
1992-01-01
This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles
Axiomatic conformal field theory
International Nuclear Information System (INIS)
Gaberdiel, M.R.; Goddard, P.
2000-01-01
A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, Moebius invariance rather than full conformal invariance is required but it is shown that every Moebius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. (orig.)
Antigravity and classical solutions of five-dimensional Kaluza-Klein theory
International Nuclear Information System (INIS)
Pollard, D.
1983-01-01
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)
Particles, fields and quantum theory
International Nuclear Information System (INIS)
Bongaarts, P.J.M.
1982-01-01
The author gives an introduction to the development of gauge theories of the fundamental interactions. Starting from classical mechanics and quantum mechanics the development of quantum electrodynamics and non-abelian gauge theories is described. (HSI)
Assessing difference between classical test theory and item ...
African Journals Online (AJOL)
Assessing difference between classical test theory and item response theory methods in scoring primary four multiple choice objective test items. ... All research participants were ranked on the CTT number correct scores and the corresponding IRT item pattern scores from their performance on the PRISMADAT. Wilcoxon ...
International Nuclear Information System (INIS)
Vollendorf, F.
1976-01-01
A theory is developed in which the gravitational as well as the electromagnetic field is described in a purely geometrical manner. In the case of a static central symmetric field Newton's law of gravitation and Schwarzschild's line element are derived by means of an action principle. The same principle leads to Fermat's law which defines the world lines of photons. (orig.) [de
Algebraic quantum field theory, perturbation theory, and the loop expansion
International Nuclear Information System (INIS)
Duetsch, M.; Fredenhagen, K.
2001-01-01
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)
Classical and Quantum Nonlinear Integrable Systems: Theory and Application
International Nuclear Information System (INIS)
Brzezinski, Tomasz
2003-01-01
This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical
Theoretical physics. Field theory
International Nuclear Information System (INIS)
Landau, L.; Lifchitz, E.
2004-01-01
This book is the fifth French edition of the famous course written by Landau/Lifchitz and devoted to both the theory of electromagnetic fields and the gravity theory. The talk of the theory of electromagnetic fields is based on special relativity and relates to only the electrodynamics in vacuum and that of pointwise electric charges. On the basis of the fundamental notions of the principle of relativity and of relativistic mechanics, and by using variational principles, the authors develop the fundamental equations of the electromagnetic field, the wave equation and the processes of emission and propagation of light. The theory of gravitational fields, i.e. the general theory of relativity, is exposed in the last five chapters. The fundamentals of the tensor calculus and all that is related to it are progressively introduced just when needed (electromagnetic field tensor, energy-impulse tensor, or curve tensor...). The worldwide reputation of this book is generally allotted to clearness, to the simplicity and the rigorous logic of the demonstrations. (A.C.)
Statistical mechanics and field theory
International Nuclear Information System (INIS)
Samuel, S.A.
1979-05-01
Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. 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. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown 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. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. 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. 64 references
Does general relativity theory possess the classical newtonian limit
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.
1980-01-01
A detailed comparison of newtonian approximation of the Einstein theory and the Newton theory of gravity is made. A difference of principle between these two theories is clarified at the stage of obtaining integrals of motion. Exact eqautions of motion and Einstein equations shows the existence only zero integrals of motion as well as in the newtonian approximation. A conclusion is that GRT has no classical newtonian limit, since the integrals of motion in the Newton theory of gravity and in the newtonian approximation of the Einstein theory do not coincide [ru
Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces
International Nuclear Information System (INIS)
Khrennikov, Andrei
2010-01-01
One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.
International Nuclear Information System (INIS)
Vajskopf, V.F.
1982-01-01
The article deals with the history of the development of quantum electrodynamics since the date of publishing the work by P.A.M. Dirac ''The Quantum Theory of the Emission and Absorption of Radiation''. Classic ''before-Dirac'' electrodynamics related with the names of Maxwell, Lorenz, Hertz, is outlined. Work of Bohr and Rosenfeld is shown to clarify the physical sense of quantized field and to reveal the existence of uncertainties between the strengths of different fields. The article points to the significance of the article ''Quantum theory of radiation'' by E. Fermi which clearly describes the Dirac theory of radiation, relativistic wave equation and fundamentals of quantum electrodynamics. Shown is work on elimination of troubles related with the existence of states with negative kinetic energy or with negative mass. Hypothesis on the Dirac filled-in vacuum led to understanding of the existence of antiparticles and two unknown till then fundamental processes - pair production and annihilation. Ways of fighting against the infinite quantities in quantum electrodynamics are considered. Renormalization of the theory overcame all the infinities and gave a pattern for calculation of any processes of electron interactions with electromagnetic field to any desired accuracy
International Nuclear Information System (INIS)
Edelen, D.G.B.
1986-01-01
Homogeneous scaling of the group space of the Poincare group, P 10 , is shown to induce scalings of all geometric quantities associated with the local action of P 10 . The field equations for both the translation and the Lorentz rotation compensating fields reduce to O(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8πGc -4 . Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to break P 10 -gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system of P 10 -gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincare gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Slavnov, A.A.
1981-01-01
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 [ru
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Energy Technology Data Exchange (ETDEWEB)
Kamenshchik, A. Yu. [Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46, 40126 Bologna (Italy) and L.D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow (Russian Federation); Manti, S. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy)
2013-02-21
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
International Nuclear Information System (INIS)
Kamenshchik, A. Yu.; Manti, S.
2013-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Classical calculation of radiative lifetimes of atomic hydrogen in a homogeneous magnetic field
International Nuclear Information System (INIS)
Horbatsch, M.W.; Hessels, E.A.; Horbatsch, M.
2005-01-01
Radiative lifetimes of hydrogenic atoms in a homogeneous magnetic field of moderate strength are calculated on the basis of classical radiation. The modifications of the Keplerian orbits due to the magnetic field are incorporated by classical perturbation theory. The model is complemented by a classical radiative decay calculation using the radiated Larmor power. A recently derived highly accurate formula for the transition rate of a field-free hydrogenic state is averaged over the angular momentum oscillations caused by the magnetic field. The resulting radiative lifetimes for diamagnetic eigenstates classified by n,m and the diamagnetic energy shift C compare well with quantum results
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...
Parafermionic conformal field theory
International Nuclear Information System (INIS)
Kurak, V.
1989-09-01
Conformal parafermionic field theories are reviewed with emphasis on the computation of their OPE estructure constants. It is presented a simple computational of these for the Z(N) parafermions, unveilling their Lie algebra content. (A.C.A.S.) [pt
International Nuclear Information System (INIS)
Cadavid, A.C.
1989-01-01
The author constructs a non-Abelian field theory by gauging a Kac-Moody algebra, obtaining an infinite tower of interacting vector fields and associated ghosts, that obey slightly modified Feynman rules. She discusses the spontaneous symmetry breaking of such theory via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra. She proceeds to show that there is no obstacle in implementing the affine extension of supersymmetric Yang-Mills theories. The result is valid in four, six and ten space-time dimensions. Then the affine extension of supergravity is investigated. She discusses only the loop algebra since the affine extension of the super-Poincare algebra appears inconsistent. The construction of the affine supergravity theory is carried out by the group manifold method and leads to an action describing infinite towers of spin 2 and spin 3/2 fields that interact subject to the symmetries of the loop algebra. The equations of motion satisfy the usual consistency check. Finally, she postulates a theory in which both the vector and scalar fields lie in the loop algebra of SO(3). This theory has an expanded soliton sector, and corresponding to the original 't Hooft-Polyakov solitonic solutions she now finds an infinite family of exact, special solutions of the new equations. She also proposes a perturbation method for obtaining an arbitrary solution of those equations for each level of the affine index
Comparison of Classical Test Theory and Item Response Theory in Individual Change Assessment
Jabrayilov, Ruslan; Emons, Wilco H. M.; Sijtsma, Klaas
2016-01-01
Clinical psychologists are advised to assess clinical and statistical significance when assessing change in individual patients. Individual change assessment can be conducted using either the methodologies of classical test theory (CTT) or item response theory (IRT). Researchers have been optimistic
International Nuclear Information System (INIS)
Efimov, G.V.
1976-01-01
The basic ideas for creating the theory of nonlocal interactions of a scalar one-component field are presented. Lagrangian describing a non-interacting field is the ordinary one so that non-interacting particles are described by standard methods of the Fock space. Form factors introduced have been chosen from a class of analytic functionals and quantized. Conditions of microcausality have been considered in detail. The convergence of all integrals corresponding to the arbitrary Feynman diagrams in spinor electrodynamics is guaranteed in the frame of the rules formulated. It is noted in conclusion that the spinor electrodynamics with nonlocal interaction contains no ultraviolet divergencies and satisfies all the requirements of the quantum field theory; in this sense it is mathematically more consistent than its local version
Holographic effective field theories
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei' , Università di Padova,and INFN - Sezione di Padova, Via Marzolo 8, I-35131 Padova (Italy); Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,and INFN - Sezione di Milano-Bicocca, I-20126 Milano (Italy)
2016-06-28
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.
Aesthetic Creativity: Insights from Classical Literary Theory on Creative Learning
Hellstrom, Tomas Georg
2011-01-01
This paper addresses the subject of textual creativity by drawing on work done in classical literary theory and criticism, specifically new criticism, structuralism and early poststructuralism. The question of how readers and writers engage creatively with the text is closely related to educational concerns, though they are often thought of as…
On the background independence of string field theory
International Nuclear Information System (INIS)
Sen, A.
1990-01-01
Given a solution Ψ cl of the classical equations of motion in either closed or open string field theory formulated around a given conformal field theory background, we can construct a new operator Q B in the corresponding two-dimensional field theory such that (Q B ) 2 =0. It is shown that in the limit when the background field Ψ cl is weak, Q B can be identified with the BRST charge of a new local conformal field theory. This indicates that the string field theories formulated around these two different conformal field theories are actually the same theory, and that these two conformal field theories may be regarded as different classical solutions of this string field theory. (orig.)
Introduction to algebraic quantum field theory
International Nuclear Information System (INIS)
Horuzhy, S.S.
1990-01-01
This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs
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...
Mathematical theories of classical particle channeling in perfect crystals
International Nuclear Information System (INIS)
Dumas, H. Scott
2005-01-01
We present an overview of our work on rigorous mathematical theories of channeling for highly energetic positive particles moving in classical perfect crystal potentials. Developed over the last two decades, these theories include: (i) a comprehensive, highly mathematical theory based on Nekhoroshev's theorem which embraces both axial and planar channeling as well as certain non-channeling particle motions (ii) a theory of axial channeling for relativistic particles based on a single-phase averaging method for ordinary differential equations and (iii) a theory of planar channeling for relativistic particles based on a two-phase averaging method for ordinary differential equations. Here we touch briefly on (i) and (ii), then focus on (iii). Together these theories place Lindhard's continuum model approximations on a firm mathematical foundation, and should serve as the starting point for more refined mathematical treatments of channeling
Introduction to string field theory
International Nuclear Information System (INIS)
Horowitz, G.T.
1989-01-01
A light cone gauge superstring field theory is constructed. The BRST approach is described discussing generalizations to yield gauge invariant free superstring field theory and interacting theory for superstrings. The interaction term is explicitly expressed in terms of first quantized oscillators. A purily cubic action for superstring field theory is also derived. (author)
Grassmann expansion of the classical N=2 supergravity field equations
International Nuclear Information System (INIS)
Embacher, F.
1984-01-01
The classical field equations of N=2 supergravity are expanded with respect to an infinite dimensional Grassmann algebra. The general freedom in constructing classical solution is exhibited. As an application, a uniqueness theorem for supersymmetric extreme black holes is given. (Author)
International Nuclear Information System (INIS)
Sugama, H.
1999-08-01
The Lagrangian formulation of the gyrokinetic theory is generalized in order to describe the particles' dynamics as well as the self-consistent behavior of the electromagnetic fields. The gyrokinetic equation for the particle distribution function and the gyrokinetic Maxwell's equations for the electromagnetic fields are both derived from the variational principle for the Lagrangian consisting of the parts of particles, fields, and their interaction. In this generalized Lagrangian formulation, the energy conservation property for the total nonlinear gyrokinetic system of equations is directly shown from the Noether's theorem. This formulation can be utilized in order to derive the nonlinear gyrokinetic system of equations and the rigorously conserved total energy for fluctuations with arbitrary frequency. (author)
Foundations of quantum theory from classical concepts to operator algebras
Landsman, Klaas
2017-01-01
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.
Cavity quantum chromodynamics in the presence of a classical background field
International Nuclear Information System (INIS)
Gavin, E.J.O.; Viollier, R.D.
1988-01-01
The QCD (quantum chromodynamics) Lagrange density is constructed in which the gluon field has a classical part, using the background field gauge. The conserved currents deriving from the symmetries of this theory are given and used to define boundary conditions on the field operators on the surface of a spherical, static cavity. The field operators are expanded in terms of a complete set of cavity modes that satisfy the boundary conditions and the field equations in the Dirac picture. 13 refs
Classic Grounded Theory to Analyse Secondary Data: Reality and Reflections
Directory of Open Access Journals (Sweden)
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.
Classical theory of atom-surface scattering: The rainbow effect
Miret-Artés, Salvador; Pollak, Eli
2012-07-01
The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.
International Nuclear Information System (INIS)
Green, M.B.
1984-01-01
Superstring field theories are formulated in terms of light-cone-gauge superfields that are functionals of string coordinates chi(sigma) and theta(sigma). The formalism used preserves only the manifest SU(4) symmetry that corresponds to rotations among six of the eight transverse directions. In type I theories, which have one ten-dimensional supersymmetry and describe both open and closed strings, there are five interaction terms of two basic kinds. One kind is a breaking or joining interaction, which is a string generalization of a cubic Yang-Mills coupling. It is relevant to both the three open-string vertex and the open-string to closed-string transition vertex. The other kind is an exchange or crossing-over interaction, which is a string generalization of a cubic gravitational coupling. All the interactions can be uniquely determined by requiring continuity of the coordinates chi(sigma) and theta(sigma) (which implies local conservation of the conjugate momenta) and by imposing the global supersymmetry algebra. Specific local operators are identified for each of the two kinds of interactions. In type II theories, which have two ten-dimensional supersymmetries and contain closed strings only, the entire interaction hamiltonian consists of a single cubic vertex. The higher-order contact terms of the N=8 supergravity theory that arises in the low-energy limit give an effective description of the exchange of massive string modes. (orig.)
From quantum gravity to quantum field theory via noncommutative geometry
International Nuclear Information System (INIS)
Aastrup, Johannes; Grimstrup, Jesper Møller
2014-01-01
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)
Instantons in Lifshitz field theories
Energy Technology Data Exchange (ETDEWEB)
Fujimori, Toshiaki; Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2015-10-05
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for “the superpotential” defining “the detailed balance condition”. The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.
Statistical mechanics of lattice Boson field theory
International Nuclear Information System (INIS)
1976-01-01
A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3 and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region
Statistical mechanics of lattice boson field theory
International Nuclear Information System (INIS)
Baker, G.A. Jr.
1977-01-01
A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3, and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region. 24 references
A superfield generalization of the classical action-at-a-distance theory
International Nuclear Information System (INIS)
Tugai, V.V.; Zheltukhin, A.A.
1994-07-01
A generalization of the Fokker-Schwarzschild-Tetrode-Wheeler-Feynman electromagnetic theory onto the superspace is considered. The classical vector and spinor fields belonging to the Maxwell supermultiplet are built of the world-line coordinates of the charged particles in superspace. (author). 9 refs
International Nuclear Information System (INIS)
Barut, A.O.; Cruz, M.G.
1992-08-01
We use the method of analytic continuation of the equation of motion including the self-fields to evaluate the radiation reaction for a classical relativistic spinning point particle in interaction with scalar, tensor and linearized gravitational fields in flat spacetime. In the limit these equations reduce to those of spinless particles. We also show the renormalizability of these theories. (author). 10 refs
Karpilovsky, G
1989-01-01
This monograph gives a systematic account of certain important topics pertaining to field theory, including the central ideas, basic results and fundamental methods.Avoiding excessive technical detail, the book is intended for the student who has completed the equivalent of a standard first-year graduate algebra course. Thus it is assumed that the reader is familiar with basic ring-theoretic and group-theoretic concepts. A chapter on algebraic preliminaries is included, as well as a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.
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.
Introduction to gauge field theory
International Nuclear Information System (INIS)
Bailin, D.; Love, A.
1986-01-01
This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications
Superstring field theory equivalence: Ramond sector
International Nuclear Information System (INIS)
Kroyter, Michael
2009-01-01
We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.
A classical density functional theory of ionic liquids.
Forsman, Jan; Woodward, Clifford E; Trulsson, Martin
2011-04-28
We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.
International Nuclear Information System (INIS)
Mancini, F.
1986-01-01
Theoretical physicists, coming from different countries, working on different areas, gathered at Positano: the Proceedings contain all the lectures delivered as well as contributed papers. Many areas of physics are represented, elementary particles in high energy physics, quantum relativity, quantum geometry, condensed matter physics, statistical mechanics; but all works are concerned with the use of the methods of quantum field theory. The first motivation of the meeting was to pay homage to a great physicist and a great friend; it was also an occasion in which theoretical physicists got together to discuss and to compare results in different fields. The meeting was very intimate; the relaxed atmosphere allowed constructive discussions and contributed to a positive exchange of ideas. (orig.)
On Multi-Point Liouville Field Theory
International Nuclear Information System (INIS)
Zarrinkamar, S.; Rajabi, A. A.; Hassanabadi, H.
2013-01-01
In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or at least require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field. (author)
Towards quantum gravity via quantum field theory. Problems and perspectives
Energy Technology Data Exchange (ETDEWEB)
Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2016-07-01
General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.
Digestible quantum field theory
Smilga, Andrei
2017-01-01
This book gives an intermediate level treatment of quantum field theory, appropriate to a reader with a first degree in physics and a working knowledge of special relativity and quantum mechanics. It aims to give the reader some understanding of what QFT is all about, without delving deep into actual calculations of Feynman diagrams or similar. The author serves up a seven‐course menu, which begins with a brief introductory Aperitif. This is followed by the Hors d'oeuvres, which set the scene with a broad survey of the Universe, its theoretical description, and how the ideas of QFT developed during the last century. In the next course, the Art of Cooking, the author recaps on some basic facts of analytical mechanics, relativity, quantum mechanics and also presents some nutritious “extras” in mathematics (group theory at the elementary level) and in physics (theory of scattering). After these preparations, the reader should have a good appetite for the Entrées ‐ the central par t of the book where the...
Phase-space quantization of field theory
International Nuclear Information System (INIS)
Curtright, T.; Zachos, C.
1999-01-01
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999
Outline of a classical theory of quantum physics and gravitation
International Nuclear Information System (INIS)
Gallop, J.W.
1975-01-01
It is argued that in the manner in which the Galilean-Newtonian physics may be said to have explained the Ptolemaic-Copernican theories in terms which have since been called classical, so also Milner's theories of the structure of matter may be said to explain present day quantum and relativistic theory. In both cases the former employ the concept of force and the latter, by contrast, are geometrical theories. Milner envisaged space as being stressed, whereas Einstein thought of it as strained. Development of Milner's theory from criticisms and suggestions made by Kilmister has taken it further into the realms of quantum and gravitational physics, where it is found to give a more physically comprehensible explanation of the phenomena. Further, it shows why present day quantum theory is cast in a statistical form. The theory is supported by many predictions such as the ratio of Planck's constant to the mass of the electron, the value of the fine structure constant and reason for apparent variations in past measurements, the magnetic moment of the electron and proton of the stable particles such as the neutron Λ and Σ together with the kaon, and a relation between the universal gravitational constant and Hubble's constant - all within published experimental accuracy. The latest results to be accounted for by the theory are the masses of the newly discovered psi particles and confirmation of the value of the decay of Newton's gravitational constant obtained from lunar measurements. (author)
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
Quantum golden field theory - Ten theorems and various conjectures
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
Ten theorems and few conjectures related to quantum field theory as applied to high energy physics are presented. The work connects classical quantum field theory with the golden mean renormalization groups of non-linear dynamics and E-Infinity theory
Quantum field theory and the standard model
Schwartz, Matthew D
2014-01-01
Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduate-level understanding of quantum mechanics, the book steadily develops the Standard Model and state-of-the-art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and end-of-chapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independe...
Electromagnetic Field Theory A Collection of Problems
Mrozynski, Gerd
2013-01-01
After a brief introduction into the theory of electromagnetic fields and the definition of the field quantities the book teaches the analytical solution methods of Maxwell’s equations by means of several characteristic examples. The focus is on static and stationary electric and magnetic fields, quasi stationary fields, and electromagnetic waves. For a deeper understanding, the many depicted field patterns are very helpful. The book offers a collection of problems and solutions which enable the reader to understand and to apply Maxwell’s theory for a broad class of problems including classical static problems right up to waveguide eigenvalue problems. Content Maxwell’s Equations - Electrostatic Fields - Stationary Current Distributions – Magnetic Field of Stationary Currents – Quasi Stationary Fields: Eddy Currents - Electromagnetic Waves Target Groups Advanced Graduate Students in Electrical Engineering, Physics, and related Courses Engineers and Physicists Authors Professor Dr.-Ing. Gerd Mrozynski...
Logarithmic conformal field theory
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Colour Constancy Beyond the Classical Receptive Field.
Akbarinia, Arash; Parraga, C Alejandro
2017-09-18
The problem of removing illuminant variations to preserve the colours of objects (colour constancy) has already been solved by the human brain using mechanisms that rely largely on centre-surround computations of local contrast. In this paper we adopt some of these biological solutions described by long known physiological findings into a simple, fully automatic, functional model (termed Adaptive Surround Modulation or ASM). In ASM, the size of a visual neuron's receptive field (RF) as well as the relationship with its surround varies according to the local contrast within the stimulus, which in turn determines the nature of the centre-surround normalisation of cortical neurons higher up in the processing chain. We modelled colour constancy by means of two overlapping asymmetric Gaussian kernels whose sizes are adapted based on the contrast of the surround pixels, resembling the change of RF size. We simulated the contrast-dependent surround modulation by weighting the contribution of each Gaussian according to the centre-surround contrast. In the end, we obtained an estimation of the illuminant from the set of the most activated RFs' outputs. Our results on three single-illuminant and one multi-illuminant benchmark datasets show that ASM is highly competitive against the state-of-the-art and it even outperforms learning-based algorithms in one case. Moreover, the robustness of our model is more tangible if we consider that our results were obtained using the same parameters for all datasets, that is, mimicking how the human visual system operates. These results might provide an insight on how dynamical adaptation mechanisms contribute to make object's colours appear constant to us.
On background-independent open-string field theory
International Nuclear Information System (INIS)
Witten, E.
1992-01-01
A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ''space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant open-string world-sheet theories and that, when expanding around a classical solution, the infinitesimal gauge transformations are generated by the world-sheet BRST operator
International Nuclear Information System (INIS)
Velasco, E.S.
1986-01-01
This dissertation deals with several topics of field theory. Chapter I is a brief outline of the work presented in the next chapters. In chapter II, the Gauss-Bonnet-Chern theorem for manifolds with boundary is computed using the path integral representation of the Witten index for supersymmetric quantum mechanical systems. In chapter III the action of N = 2 (Poincare) supergravity is obtained in terms of N = 1 superfields. In chapter IV, N = 2 supergravity coupled to the (abelian) vector multiplet is projected into N - 1 superspace. There, the resulting set of constraints is solved in terms of unconstrained prepotential and the action in terms of N = 1 superfields is constructed. In chapter V the set of constraints for N = 2 conformal supergravity is projected into N = 1 superspace and solved in terms of N = 1 conformal supergravity fields a d matter prepotentials. In chapter VI the role of magnetic monopoles in the phase structure of the change one fixed length abelian Higgs model ins the latticer is investigated using analytic and numerical methods. The technique of monopole suppression is used to determine the phase transition lines that are monopole driven. Finally in chapter VII, the role of the charge of the Higgs field in the abelian Higgs model in the lattice is investigated
Unified-field theory: yesterday, today, tomorrow
International Nuclear Information System (INIS)
Bergman, P.G.
1982-01-01
Beginning with the expounding of Einstein understanding of advantages and disadvantages of general relativity theory, the authors proceed to consideration of what the complete unified theory have to be according to Einstein. The four theories which can be considered as ''unified'', namely weyl and Calutsa ones, worked out a half of century ago, and twistor twisting and supersymmetry theories, nowadays attracting attention, are briefly described and discussed. The authors come to a conclusion that achievements in elementary-particle physics have to affect any future theory, that this theory has to explain the principle contradictions between classical and quantum field theories, and that finally it can lead to change of the modern space-time model as a four-dimensional variety
On some classical problems of descriptive set theory
International Nuclear Information System (INIS)
Kanovei, Vladimir G; Lyubetskii, Vasilii A
2003-01-01
The centenary of P.S. Novikov's birth provides an inspiring motivation to present, with full proofs and from a modern standpoint, the presumably definitive solutions of some classical problems in descriptive set theory which were formulated by Luzin [Lusin] and, to some extent, even earlier by Hadamard, Borel, and Lebesgue and relate to regularity properties of point sets. The solutions of these problems began in the pioneering works of Aleksandrov [Alexandroff], Suslin [Souslin], and Luzin (1916-17) and evolved in the fundamental studies of Goedel, Novikov, Cohen, and their successors. Main features of this branch of mathematics are that, on the one hand, it is an ordinary mathematical theory studying natural properties of point sets and functions and rather distant from general set theory or intrinsic problems of mathematical logic like consistency or Goedel's theorems, and on the other hand, it has become a subject of applications of the most subtle tools of modern mathematical logic
Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice
Directory of Open Access Journals (Sweden)
Kurkela Aleksi
2018-01-01
Full Text Available Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss’s law is conserved.
Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice
Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko
2018-03-01
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved.
Fractional Stochastic Field Theory
Honkonen, Juha
2018-02-01
Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.
Scattering of classical and quantum particles by impulsive fields
Balasin, Herbert; Aichelburg, Peter C.
2018-05-01
We investigate the scattering of classical and quantum particles in impulsive backgrounds fields. These fields model short outbursts of radiation propagating with the speed of light. The singular nature of the problem will be accounted for by the use of Colombeau’s generalized function which however give rise to ambiguities. It is the aim of the paper to show that these ambiguities can be overcome by implementing additional physical conditions, which in the non-singular case would be satisfied automatically. As example we discuss the scattering of classical, Klein–Gordon and Dirac particles in impulsive electromagnetic fields.
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Classical color fields as a dark matter candidate
Dzhunushaliev, Vladimir
2006-01-01
The model of Dark Matter is proposed in which the Dark Matter is a classical color field. The color fields are invisible as they may interact with colored elementary particles like 't Hooft - Polyakov monopole only. The comparison with the Universal Rotation Curve is carried out.
Classical Bianchi Type I Cosmology in K-Essence Theory
International Nuclear Information System (INIS)
Pimentel, Luis O.; Socorro, J.; Espinoza-García, Abraham
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 between the anisotropic parameters and the volume of the universe. We also include a qualitative analysis of the analog of the Friedmann equation.
Global effects in quaternionic quantum field theory
International Nuclear Information System (INIS)
Brumby, S.P.; Joshi, G.C.
1997-01-01
A local quaternionic gauge structure is introduced onto space-time. It is a theory of vector bosons and dimensionless scalar fields, which recalls semi-classical treatments of gravity. After transforming to the 'i' gauge, it was found that the quaternionic symmetry takes the form of an exotic SU (2) gauge theory in the standard complex framework, with global phenomena appearing in the form of cosmic strings. Coupling this quaternionic sector to the Standard Model sector has only been achieved at the level of an effective theory, which is constrained by the quaternionic origin of the bosons to be of a nonrenormalisable form. 14 refs.,
Weak values in a classical theory with an epistemic restriction
International Nuclear Information System (INIS)
Karanjai, Angela; Cavalcanti, Eric G; Bartlett, Stephen D; Rudolph, Terry
2015-01-01
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the procedure of weak measurement and postselection, and the interpretation of the associated weak value, using a theory of classical mechanics supplemented by an epistemic restriction that is known to be operationally equivalent to a subtheory of quantum mechanics. Both the real and imaginary components of the weak value appear as phase space displacements in the postselected expectation values of the measurement device's position and momentum distributions, and we recover the same displacements as in the quantum case by studying the corresponding evolution in our theory of classical mechanics with an epistemic restriction. By using this epistemically restricted theory, we gain insight into the appearance of the weak value as a result of the statistical effects of post selection, and this provides us with an operational interpretation of the weak value, both its real and imaginary parts. We find that the imaginary part of the weak value is a measure of how much postselection biases the mean phase space distribution for a given amount of measurement disturbance. All such biases proportional to the imaginary part of the weak value vanish in the limit where disturbance due to measurement goes to zero. Our analysis also offers intuitive insight into how measurement disturbance can be minimized and the limits of weak measurement. (paper)
Classical Noether theory with application to the linearly damped particle
International Nuclear Information System (INIS)
Leone, Raphaël; Gourieux, Thierry
2015-01-01
This paper provides a modern presentation of Noether’s theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close relationships between Noether symmetries and first integrals, we investigate the variational point symmetries of the Lagrangian introduced by Bateman, Caldirola and Kanai. This analysis leads to the determination of all the time-independent potentials allowing such symmetries, in the one-dimensional and the radial cases. Then we develop a symmetry-based transformation of Lagrangians into autonomous others, and apply it to our problem. To be complete, we enlarge the study to Lie point symmetries which we associate logically to the Noether ones. Finally, we succinctly address the issue of a ‘weakened’ Noether’s theory, in connection with ‘on-flows’ symmetries and non-local constant of motions, because it has a direct physical interpretation in our specific problem. Since the Lagrangian we use gives rise to simple calculations, we hope that this work will be of didactic interest to graduate students, and give teaching material as well as food for thought for physicists regarding Noether’s theory and the recent developments around the idea of symmetry in classical mechanics. (paper)
a Classical Isodual Theory of Antimatter and its Prediction of Antigravity
Santilli, Ruggero Maria
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 treatment of matter and antimatter in due time, and as the classical foundations of an axiomatically consistent inclusion of gravitation in unified gauge theories recently appeared elsewhere, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with corresponding formulations at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is antiautomorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also antiautomorphic (and more generally, antiisomorphic), yet it is applicable beginning at the classical level and then persists at the quantum level where it becomes equivalent to charge conjugation. We therefore present, apparently for the first time, the classical isodual theory of antimatter, we identify the physical foundations of the theory as being the novel isodual Galilean, special and general relativities, and we show the compatibility of the theory with all available classical experimental data on antimatter. We identify the classical foundations of the prediction of antigravity for antimatter in the field of matter (or vice-versa) without any claim on its validity, and defer its resolution to specifically identified experiments. We identify the novel, classical, isodual electromagnetic waves which are predicted to be emitted by antimatter, the so-called space-time machine based on a novel non-Newtonian geometric propulsion, and other implications of the theory. We also introduce, apparently for the first time, the isodual space and time inversions and show that they are nontrivially different than the conventional ones, thus
A possibilistic uncertainty model in classical reliability theory
International Nuclear Information System (INIS)
De Cooman, G.; Capelle, B.
1994-01-01
The authors argue that a possibilistic uncertainty model can be used to represent linguistic uncertainty about the states of a system and of its components. Furthermore, the basic properties of the application of this model to classical reliability theory are studied. The notion of the possibilistic reliability of a system or a component is defined. Based on the concept of a binary structure function, the important notion of a possibilistic function is introduced. It allows to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components
Kohli, Nidhi; Koran, Jennifer; Henn, Lisa
2015-01-01
There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior…
The Prediction of Item Parameters Based on Classical Test Theory and Latent Trait Theory
Anil, Duygu
2008-01-01
In this study, the prediction power of the item characteristics based on the experts' predictions on conditions try-out practices cannot be applied was examined for item characteristics computed depending on classical test theory and two-parameters logistic model of latent trait theory. The study was carried out on 9914 randomly selected students…
Critical behavior in a random field classical Heisenberg model for amorphous systems
International Nuclear Information System (INIS)
Albuquerque, Douglas F. de; Alves, Sandro Roberto L.; Arruda, Alberto S. de
2005-01-01
By using the differential operator technique and the effective field theory scheme, the critical behavior of amorphous classical Heisenberg ferromagnet of spin-1/2 in a random field is studied. The phase diagram in the T-H and T-α planes on a simple cubic lattice for a cluster with two spins is obtained. Tricritical points, reentrant phenomena and influence of the random field and amorphization on the transition temperature are discussed
Stochastic theory for classical and quantum mechanical systems
International Nuclear Information System (INIS)
Pena, L. de la; Cetto, A.M.
1975-01-01
From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section
Marshaling Resources: A Classic Grounded Theory Study of Online Learners
Directory of Open Access Journals (Sweden)
Barbara Yalof
2014-06-01
Full Text Available Classic grounded theory (CGT was used to identify a main concern of online students in higher education. One of the main impediments to studying online is a sense of isolation and lack of access to support systems as students navigate through complex requirements of their online programs. Hypothetical probability statements illustrate the imbalance between heightened needs of virtual learners and perceived inadequate support provided by educational institutions. The core variable, marshaling resources, explains how peer supports sustain motivation toward successful program completion. Understanding the critical contribution virtual interpersonal networks make towards maximizing resources by group problem solving is a significant aspect of this theory. Keywords: Online learning, e-learning, personal learning networks, peer networks
Classical theory of rotational rainbow scattering from uncorrugated surfaces
International Nuclear Information System (INIS)
Khodorkovsky, Yuri; Averbukh, Ilya Sh; Pollak, Eli
2010-01-01
A classical perturbation theory is developed to study rotational rainbow scattering of molecules from uncorrugated frozen surfaces. Considering the interaction of the rigid rotor with the translational motion towards the surface to be weak allows for a perturbative treatment, in which the known zeroth order motion is that of a freely rotating molecule hitting a surface. Using perturbation theory leads to explicit expressions for the angular momentum deflection function with respect to the initial orientational angle of the rotor that are valid for any magnitude of the initial angular momentum. The rotational rainbows appear as peaks both in the final angular momentum and rotational energy distributions, as well as peaks in the angular distribution, although the surface is assumed to be uncorrugated. The derived analytic expressions are compared with numerical simulation data. Even when the rotational motion is significantly coupled to the translational motion, the predictions of the perturbative treatment remain qualitatively correct.
Stochastic quantization of the Kink solution of phi4 field theory
International Nuclear Information System (INIS)
Kates, R.; Rosenblum, A.
1989-01-01
The method of Parisi-Wu Stochastic quantization in quantum field theory is compared to earlier work in classical field equations. The method is applied to solve for the propagator for Phi 4 field theory by perturbing the Kink solution
Symmetries of noncommutative scalar field theory
International Nuclear Information System (INIS)
De Goursac, Axel; Wallet, Jean-Christophe
2011-01-01
We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit.
Anthropology and social theory: renewing dialogue via the classics
DEFF Research Database (Denmark)
Thomassen, Bjørn
2011-01-01
Agnes Horvath, Bjørn Thomassen, & Dr Harald Wydra, editors of the Journal,International Political Anthropology “Anthropology and social theory: renewing dialogue via the classics” This paper argues that anthropology may represent a perspective from where social theory can renew itself. The presen......Agnes Horvath, Bjørn Thomassen, & Dr Harald Wydra, editors of the Journal,International Political Anthropology “Anthropology and social theory: renewing dialogue via the classics” This paper argues that anthropology may represent a perspective from where social theory can renew itself...... simply representing a view from "below", a politically correct appreciation of cultural diversity, or a taste for the exotic and marginal. It involves, we argue, attention towards key theoretical concepts developed within "classical" anthropology that uniquely facilitate a proper understanding...... in mechanical rationalisation on the one hand, and the mere stimulation of the senses on the other, guided by an exclusively materialistic and utilitarian vision of the human being and its social environment, it is possible to take inspiration from Antiquity in order to spark a renewal badly needed...
Quantum field theory in a semiotic perspective
International Nuclear Information System (INIS)
Dosch, H.G.
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, Poincare, 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 account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)
Quantum field theory in a semiotic perspective
Energy Technology Data Exchange (ETDEWEB)
Dosch, H.G. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Mueller, V.F. [Technische Univ. Kaiserslautern (Germany). Fachbereich Physik; Sieroka, N. [Zurich Univ. (Switzerland)
2005-07-01
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, Poincare, 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 account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs
Neutrino fields in Einstein-Cartan theory
International Nuclear Information System (INIS)
Griffiths, J.B.
1981-01-01
The spin-coefficient formalism presented elsewhere is here applied to classical neutrino fields in Einstein-Cartan theory. It is shown that the neutrino current vector is tangent to an expansion-free null geodesic congruence with constant and equal twist and shear, which vanish if and only if the congruence is a repeated principal null congruence of the gravitational field. The geodesics are both extremals and autoparallels. All exact solutions for the case of pure radiation fields are obtained, and it is shown that the only possible ghost solutions have a plane wave metric. (author)
Integrable structures in quantum field theory
International Nuclear Information System (INIS)
Negro, Stefano
2016-01-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q -operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only. (topical review)
Naturality in conformal field theory
International Nuclear Information System (INIS)
Moore, G.; Seiberg, N.
1989-01-01
We discuss constraints on the operator product coefficients in diagonal and nondiagonal rational conformal field theories. Nondiagonal modular invariants always arise from automorphisms of the fusion rule algebra or from extensions of the chiral algebra. Moreover, when the chiral algebra has been maximally extended a strong form of the naturality principle of field theory can be proven for rational conformal field theory: operator product coefficients vanish if and only if the corresponding fusion rules vanish; that is, if and only if the vanishing can be understood in terms of a symmetry. We illustrate these ideas with several examples. We also generalize our ideas about rational conformal field theories to a larger class of theories: 'quasi-rational conformal field theories' and we explore some of their properties. (orig.)
Unitary unified field theories
International Nuclear Information System (INIS)
Sudarshan, E.C.G.
1976-01-01
This is an informal exposition of some recent developments. Starting with an examination of the universality of electromagnetic and weak interactions, the attempts at their unification are outlined. The theory of unitary renormalizable self-coupled vector mesons with dynamical sources is formulated for a general group. With masses introduced as variable parameters it is shown that the theory so defined is indeed unitary. Diagrammatic rules are developed in terms of a chosen set of fictitious particles. A number of special examples are outlined including a theory with strongly interacting vector and axial vector mesons and weak mesons. Applications to weak interactions of strange particles is briefly outlined. (Auth.)
Information flow, causality, and the classical theory of tachyons
International Nuclear Information System (INIS)
Basano, L.
1977-01-01
Causal paradoxes arising in the tachyon theory have been systematically solved by using the reinterpretation principle as a consequence of which cause and effect no longer retain an absolute meaning. However, even in the tachyon theory, a cause is always seen to chronologically precede its effect, but this is obtained at the price of allowing cause and effect to be interchanged when required. A recent result has shown that this interchange-ability of cause and effect must not be unlimited if heavy paradoxes are to be avoided. This partial recovery of the classical concept of causality has been expressed by the conjecture that transcendent tachyons cannot be absorbed by a tachyon detector. In this paper the directional properties of the flow of information between two observers in relative motion and its consequences on the logical self-consistency of the theory of superluminal particles are analyzed. It is shown that the above conjecture does not provide a satisfactory solution to the problem because it implies that tachyons of any speed cannot be intercepted by the same detector. (author)
Classical radiation zeros in gauge-theory amplitudes
International Nuclear Information System (INIS)
Brown, R.W.; Kowalski, K.L.; Brodsky, S.J.
1983-01-01
The electromagnetic radiation from classical convection currents in relativistic n-particle collisions is shown to vanish in certain kinematical zones, due to complete destructive interference of the classical radiation patterns of the incoming and outgoing charged lines. We prove that quantum tree photon amplitudes vanish in the same zones, at arbitrary photon momenta including spin, seagull, and internal-line currents, provided only that the electromagnetic couplings and any other derivative couplings are as prescribed by renormalizable local gauge theory (spins + #betta# is thus explained and examples with more particles are discussed. Conditions for the null zones to lie in physical regions are established. A new radiation representation, with the zeros manifest and of practical utility independently of whether the null zones are in physical regions is derived for the complete single-photon amplitude in tree approximation, using a gauge-invariant vertex expansion stemming from new internal-radiation decomposition identities. The question of whether amplitudes with closed loops can vanish in null zones is addressed. The null zone and these relations are discussed in terms of the Bargmann-Michel-Telegdi equation. The extension from photons to general massless gauge bosons is carried out
Quantized Dirac field interacting with a classical Maxwell field
International Nuclear Information System (INIS)
Kolsrud, M.
1987-10-01
The S operator for the quantized and the s matrix for the unquantized Dirac field, both fields interacting with an unquantized Maxwell field, are shown to be related in the following way: S=exp(-ic†kc) and s=exp(-ik). Here c is the column matrix of the particle operators, and k is a Hermitian matrix. With splitting of c into an electron and a positron part, a corresponding factorization of S is performed. Exact expressions for the probability amplitude for various electron and/or positron processes are then obtained
Complex analysis fundamentals of the classical theory of functions
Stalker, John
1998-01-01
This clear, concise introduction to the classical theory of one complex variable is based on the premise that "anything worth doing is worth doing with interesting examples." The content is driven by techniques and examples rather than definitions and theorems. This self-contained monograph is an excellent resource for a self-study guide and should appeal to a broad audience. The only prerequisite is a standard calculus course. The first chapter deals with a beautiful presentation of special functions. . . . The third chapter covers elliptic and modular functions. . . in much more detail, and from a different point of view, than one can find in standard introductory books. . . . For [the] subjects that are omitted, the author has suggested some excellent references for the reader who wants to go through these topics. The book is read easily and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference. ---Mathematical Reviews Mainly or...
Classical mechanics including an introduction to the theory of elasticity
Hentschke, Reinhard
2017-01-01
This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory...
A two-parameter extension of classical nucleation theory
Lutsko, James F.; Durán-Olivencia, Miguel A.
2015-06-01
A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard classical nucleation theory (CNT). The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that CNT underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier.
A two-parameter extension of classical nucleation theory
International Nuclear Information System (INIS)
Lutsko, James F; Durán-Olivencia, Miguel A
2015-01-01
A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard classical nucleation theory (CNT). The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that CNT underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier. (paper)
Field theory approach to gravitation
International Nuclear Information System (INIS)
Yilmaz, H.
1978-01-01
A number of authors considered the possibility of formulating a field-theory approach to gravitation with the claim that such an approach would uniquely lead to Einstein's theory of general relativity. In this article it is shown that the field theory approach is more generally applicable and uniqueness cannot be claimed. Theoretical and experimental reasons are given showing that the Einsteinian limit appears to be unviable
Les Houches lectures on large N field theories and gravity
International Nuclear Information System (INIS)
Maldacena, J.
2002-01-01
We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions. (authors)
On the History of Unified Field Theories
Directory of Open Access Journals (Sweden)
Goenner Hubert F.M.
2004-01-01
Full Text Available This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin - with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger's or Dirac's equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopocraphical remarks are included.
Fundamental Elements and Interactions of Nature: A Classical Unification Theory
Directory of Open Access Journals (Sweden)
Tianxi Zhang
2010-04-01
Full Text Available A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are considered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interaction between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges, weak (between electric and color charges, and strong (between color charges interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation-color charge interactions. Among the four fundamental elements, there are ten (six real and four imaginary fundamental interactions. This classical unification theory deepens our understanding of the nature fundamental elements and interactions, develops a new concept of imaginary energy for electric and color charges, and provides a
Fundamental Elements and Interactions of Nature: A Classical Unification Theory
Directory of Open Access Journals (Sweden)
Zhang T. X.
2010-04-01
Full Text Available A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are con- sidered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interac- tion between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges, weak (between electric and color charges, and strong (between color charges interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation- color charge interactions. Among the four fundamental elements, there are ten (six real and four imaginary fundamental interactions. This classical unification theory deep- ens our understanding of the nature fundamental elements and interactions, develops a new concept of imaginary energy for electric and color charges, and provides a
Methods of thermal field theory
Energy Technology Data Exchange (ETDEWEB)
Mallik, S [Saha Institute of Nuclear Physics, Calcutta (India)
1998-11-01
We introduce the basic ideas of thermal field theory and review its path integral formulation. We then discuss the problems of QCD theory at high and at low temperatures. At high temperature the naive perturbation expansion breaks down and is cured by resummation. We illustrate this improved perturbation expansion with the g{sup 2}{phi}{sup 4} theory and then sketch its application to find the gluon damping rate in QCD theory. At low temperature the hadronic phase is described systematically by the chiral perturbation theory. The results obtained from this theory for the quark and the gluon condensates are discussed. (author) 22 refs., 6 figs.
Polymer quantization of the free scalar field and its classical limit
Energy Technology Data Exchange (ETDEWEB)
Laddha, Alok; Varadarajan, Madhavan, E-mail: alok@rri.res.i, E-mail: madhavan@rri.res.i [Raman Research Institute, Bangalore 560 080 (India)
2010-09-07
Building on prior work, a generally covariant reformulation of a free scalar field theory on the flat Lorentzian cylinder is quantized using loop quantum gravity (LQG)-type 'polymer' representations. This quantization of the continuum classical theory yields a quantum theory which lives on a discrete spacetime lattice. We explicitly construct a state in the polymer Hilbert space which reproduces the standard Fock vacuum two-point functions for long-wavelength modes of the scalar field. Our construction indicates that the continuum classical theory emerges under coarse graining. All our considerations are free of the 'triangulation' ambiguities which plague attempts to define quantum dynamics in LQG. Our work constitutes the first complete LQG-type quantization of a generally covariant field theory together with a semi-classical analysis of the true degrees of freedom and thus provides a perfect infinite-dimensional toy model to study open issues in LQG, particularly those pertaining to the definition of quantum dynamics.
International Nuclear Information System (INIS)
Castro, A; Gross, E K U
2014-01-01
We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wavefunction, can be simplified by making use of time-dependent density-functional theory. In this case, the optimal control equations require some modifications that we will provide. The abstract general formulation is complemented with the simple example of the H 2 + molecule in the presence of a laser field. (paper)
Introduction to quantum field theory
Alvarez-Gaumé, Luís
1994-01-01
The purpose of this lecture is to review some elementary aspects of Quantum Field Theory. From the necessity to introduce quantum fields once quantum mechanics and special relativity are put together, to some of the basic practical computational tools in the subject, including the canonical quantization of simple field theories, the derivation of Feynman rules, computation of cross sections and decay rates, some introductory remarks on the treatment of unstable states and the possible realization of symmetries in a general field theory. The audience is required to have a working knowledge of quantum mechanics and special relativity and it would also be desirable to know the rudiments of relativistic quantum mechanics.
Field theory of large amplitude collective motion. A schematic model
International Nuclear Information System (INIS)
Reinhardt, H.
1978-01-01
By using path integral methods the equation for large amplitude collective motion for a schematic two-level model is derived. The original fermion theory is reformulated in terms of a collective (Bose) field. The classical equation of motion for the collective field coincides with the time-dependent Hartree-Fock equation. Its classical solution is quantized by means of the field-theoretical generalization of the WKB method. (author)
Elementary quantum field theory
International Nuclear Information System (INIS)
Thirring, W.; Henley, E.M.
1975-01-01
The first section of the book deals with the mathematical and physical description of a quantum field with the Bose-Einstein statistics and discusses observables, invariants of the field, and inner symmetries. The second section develops further methods for solvable interactions of a quantum field with static source. Section 3 explains with the aid of the Chew-Low model especially pion-nucleon scattering, static properties of nucleons, electromagnetic phenomena, and nuclear forces. (BJ/LN) [de
Quantum dynamics in transverse-field Ising models from classical networks
Directory of Open Access Journals (Sweden)
Markus Schmitt, Markus Heyl
2018-02-01
Full Text Available The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
International Nuclear Information System (INIS)
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-01-01
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined
The Nonlinear Field Space Theory
Energy Technology Data Exchange (ETDEWEB)
Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)
2016-08-10
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
International Nuclear Information System (INIS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-01-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
[Topics in field theory and string theory
International Nuclear Information System (INIS)
1990-01-01
In the past year, I have continued to investigate the relations between conformal field theories and lattice statistical mechanical models, and in particular have been studying two dimensional models coupled to quantum gravity. I have continued as well to consider possible extension of these results to higher dimensions and potential applications in other contexts
Introduction to quantum field theory
International Nuclear Information System (INIS)
Kazakov, D.I.
1988-01-01
The lectures appear to be a continuation to the introduction to elementary principles of the quantum field theory. The work is aimed at constructing the formalism of standard particle interaction model. Efforts are made to exceed the limits of the standard model in the quantum field theory context. Grand unification models including strong and electrical weak interactions, supersymmetric generalizations of the standard model and grand unification theories and, finally, supergravitation theories including gravitation interaction to the universal scheme, are considered. 3 refs.; 19 figs.; 2 tabs
The logarithmic conformal field theories
International Nuclear Information System (INIS)
Rahimi Tabar, M.R.; Aghamohammadi, A.; Khorrami, M.
1997-01-01
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two- and three-point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any n-point function containing the logarithmic field in terms of ordinary n-point functions. Finally, we calculate the operator product expansion (OPE) coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation. (orig.)
Classical origins of stabilization in circularly polarized laser fields
International Nuclear Information System (INIS)
Chism, Will; Choi, Dae-Il; Reichl, L. E.
2000-01-01
We investigate the interaction of a two-dimensional model atom with an intense, high-frequency circularly polarized laser pulse. As the laser intensity is increased, the ionization rate initially increases, then decreases dramatically, with the electron wave function developing an asymmetric ring form which rotates with the electric field. We provide evidence that this wave form is due to localization of the electron onto nonlinear classical structures. (c) 2000 The American Physical Society
Field theory approaches to new media practices
DEFF Research Database (Denmark)
Willig, Ida; Waltorp, Karen; Hartley, Jannie Møller
2015-01-01
could benefit particularly from Pierre Bourdieu’s research on cultural production. We introduce some of the literature that concerns digital media use and has been significant for field theory’s development in this context. We then present the four thematic articles in this issue and the articles......This special issue of MedieKultur specifically addresses new media practices and asks how field theory approaches can help us understand how culture is (prod)used via various digital platforms. In this article introducing the theme of the special issue, we argue that studies of new media practices...... outside the theme, which include two translations of classic texts within communications and media research. This introductory article concludes by encouraging media scholars to embark on additional studies within a field theory framework: This framework’s comprehensive theoretical basis and ideal...
Renormalization and Interaction in Quantum Field Theory
International Nuclear Information System (INIS)
RATSIMBARISON, H.M.
2008-01-01
This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory. [fr
Study of one dimensional magnetic system via field theory
International Nuclear Information System (INIS)
Talim, S.L.
1988-04-01
We present a study of one-dimensional magnetic system using field theory methods. We studied the discreteness effects in a classical anisotropic one dimensional antiferromagnet in an external magnetic field. It is shown that for TMMC, at the temperatures and magnetic fields where most experiments have been done, the corrections are small and can be neglected. (author)
Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
Aarts, G.; Smit, J.
2000-01-01
As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function
Raykov, Tenko; Marcoulides, George A.
2016-01-01
The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…
Lectures on matrix field theory
Ydri, Badis
2017-01-01
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.
International Nuclear Information System (INIS)
Hwang, Jai-chan; Noh, Hyerim
2005-01-01
We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these varieties of gravity theories are presented in unified forms. These apply both to the scalar- and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein's gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflation and its consequent power spectra are derived in unified forms which include a wide range of inflationary scenarios based on Einstein's gravity and others
Energy Technology Data Exchange (ETDEWEB)
Maxfield, Travis [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States); Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843-4242 (United States); Sethi, Savdeep [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States)
2016-11-28
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2,0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
What is so ‘classical’ about Classical Reception? Theories, Methodologies and Future Prospects
Anastasia Bakogianni
2016-01-01
This paper delivered at the University of Rio on 3rd June 2015 seeks to explore different approaches to the most fundamental questions in classical reception studies. What is classical reception? And more particularly what is so ‘classical’ about classical reception? It discusses current trends in theory and methodology via an analysis of two cinematic receptions of the ancient story of Electra; one that proclaims its debt to a classical text while the other masks its classical connections.
What is so ‘classical’ about Classical Reception? Theories, Methodologies and Future Prospects
Directory of Open Access Journals (Sweden)
Anastasia Bakogianni
2016-06-01
Full Text Available This paper delivered at the University of Rio on 3rd June 2015 seeks to explore different approaches to the most fundamental questions in classical reception studies. What is classical reception? And more particularly what is so ‘classical’ about classical reception? It discusses current trends in theory and methodology via an analysis of two cinematic receptions of the ancient story of Electra; one that proclaims its debt to a classical text while the other masks its classical connections.
Topological field theories and duality
International Nuclear Information System (INIS)
Stephany, J.; Universidad Simon Bolivar, Caracas
1996-05-01
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs
International Nuclear Information System (INIS)
Bach, A.
1981-01-01
A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)
Finite-temperature field theory
International Nuclear Information System (INIS)
Kapusta, J.I.; Landshoff, P.V.
1989-01-01
Particle number is not conserved in relativistic theories although both lepton and baryon number are. Therefore when discussing the thermodynamics of a quantum field theory one uses the grand canonical formalism. The entropy S is maximised, keeping fixed the ensemble averages E and N of energy and lepton number. Two lagrange multipliers are introduced. (author)
Classical diffusion in a field-reversed mirror
International Nuclear Information System (INIS)
Auerbach, S.P.; Condit, W.C.
1981-01-01
Classical transport of particles and heat in field-reversed mirrors is discussed. The X-points (field nulls on axis) are shown to have no deleterious effect on transport; this conclusion is true for any transport model. For an elongated Hill's vortex equilibrium the classical diffusion coefficient is calculated analytically and used to construct an analytic solution to the transport equation for particles or energy; this yields exact results for particle and energy confinement times. These life-times are roughly 3 to 6 times shorter than previous heuristic estimates. Experimentally determined life-times are within a factor of 3 to 4 of our estimates. To assess the impact of these results on reactor designs, the authors construct an analytic reactor model in which neutral-beam input balances ion heat loss. Energy loss due to synchrotron radiation is calculated analytically and shown to be negligible, even with no wall reflection. Formulas are presented which give the reactor parameters in terms of plasma temperature, energy multiplication factor Q, and allowed neutron wall loading. The effect of anomalous resistivity is incorporated heuristically by assuming an anomalous resistivity which is enhanced by a factor A over classical resistivity. For large A the minimum power of a reactor scales as Asup(11/6). A=50 gives a reactor design which still seems reasonable, but A=200 leads to extremely large, high-power reactors. (author)
Classical transport in field reversed mirrors: reactor implications
International Nuclear Information System (INIS)
Auerbach, S.P.; Condit, W.C.
1980-01-01
Assuming that the field-reversed mirror (or the closely related spheromak) turns out to be stable, the next crucial issue is transport of particles and heat. Of particular concern is the field null on axis (the X-point), which at first glance seems to allow particles to flow out unhindered. We have evaluated the classical diffusion coefficients for particles and heat in field-reversed mirrors, with particular reference to a class of Hill's vortex models. Two fairly surprising results emerge from this study. First, the diffusion-driven flow of particles and heat is finite at the X-points. This may be traced to the geometrical constraint that the current (and hence the ion-electron drag force, which causes cross-field transport) must vanish on axis. This conclusion holds for any transport model. Second, the classical diffusion coefficient D(psi), which governs both particle and heat flux, is finite on the separatrix. Indeed, in a wide class of Hill's vortex equilibria (spherical, oblate, or prolate) D(psi) is essentially independent of psi (except for the usual factor of n
Neural fields theory and applications
Graben, Peter; Potthast, Roland; Wright, James
2014-01-01
With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, research results in the field have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, the book comprises chapters on emergent patterns, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fields to the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theory and its applications have a long-standing tradition in the mathematical and computational ...
On finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1984-01-01
The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)
International Nuclear Information System (INIS)
Shaw, J.A.; Robicheaux, F.
1998-01-01
The photoabsorption spectra of atoms in a static external electric field shows modulations from recurrences: electron waves that go out from and return to the vicinity of the atomic core. Closed-orbit theory predicts the amplitudes and phases of these modulations in terms of closed classical orbits. A classical scaling law relates the properties of a closed orbit at one energy and field strength to its properties at another energy and field strength at fixed scaled energy ε=EF -1/2 . The scaling law states that the recurrence strength of orbits along the electric field axis scale as F 1/4 . We show how this law fails near bifurcations when the effective Planck constant ℎ≡ℎF 1/4 increases with increasing field at fixed ε. The recurrences of orbits away from the axis scale as F 1/8 in accordance with the classical prediction. These deviations from the classical scaling law are important in interpreting the recurrence spectra of atoms in current experiments. This leads to an extension of the uniform approximation developed by Gao and Delos [Phys. Rev. A 56, 356 (1997)] to complex momenta. copyright 1998 The American Physical Society
International Nuclear Information System (INIS)
Ramond, P.
1987-01-01
We review the construction of the free equations of motion for open and closed strings in 26 dimensions, using the methods of the Florida Group. Differing from previous treatments, we argue that the constraint L 0 -anti L 0 =0 should not be imposed on all the fields of the closed string in the gauge invariant formalism; we show that it can be incorporated in the gauge invariant formalism at the price of being unable to extract the equations of motion from a Langrangian. We then describe our purely algebraic method to introduce interactions, which works equally well for open and closed strings. Quartic interactions are absent except in the Physical Gauge. Finally, we speculate on the role of the measure of the open string path functional. (orig.)
Quantum theory of noncommutative fields
International Nuclear Information System (INIS)
Carmona, J.M.; Cortes, J.L.; Gamboa, J.; Mendez, F.
2003-01-01
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of 'noncommutative fields'. Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given. (author)
Propositional systems in local field theories
International Nuclear Information System (INIS)
Banai, M.
1980-07-01
The authors investigate propositional systems for local field theories, which reflect intrinsically the uncertainties of measurements made on the physical system, and satisfy the isotony and local commutativity postulates of Haag and Kastler. The spacetime covariance can be implemented in natural way in these propositional systems. New techniques are introduced to obtain these propositional systems: the lattice-valued logics. The decomposition of the complete orthomodular lattice-valued logics shows that these logics are more general than the usual two-valued ones and that in these logics there is enough structure to characterize the classical and quantum, non relativistic and relativistic local field theories in a natural way. The Hilbert modules give the natural inner product ''spaces'' (modules) for the realization of the lattice-valued logics. (author)
Polyacetylene and relativistic field-theory models
International Nuclear Information System (INIS)
Bishop, A.R.; Campbell, D.K.; Fesser, K.
1981-01-01
Connections between continuum, mean-field, adiabatic Peierls-Froehlich theory in the half-filled band limit and known field theory results are discussed. Particular attention is given to the phi 4 model and to the solvable N = 2 Gross-Neveu model. The latter is equivalent to the Peierls system at a static, semi-classical level. Based on this equivalence we note the prediction of both kink and polaron solitons in models of trans-(CH)/sub x/. Polarons in cis-(CH)/sub x/ are compared with those in the trans isomer. Optical absorption from polarons is described, and general experimental consequences of polarons in (CH)/sub x/ and other conjugated polymers is discussed
Field theory approaches to new media practices
DEFF Research Database (Denmark)
Hartley, Jannie Møller; Willig, Ida; Waltorp, Karen
2015-01-01
In this article introducing the theme of the special issue we argue that studies of new media practices might benefit from especially Pierre Bourdieu’s research on cultural production. We introduce some of the literature, which deals with the use of digital media, and which have taken steps...... to develop field theory in this context. Secondly, we present the four thematic articles in this issue and the articles outside the theme, which includes two translations of classic texts within communication and media research. This introduction article concludes by encouraging media scholars to embark...... on more studies within a field theory framework, as the ability of the comprehensive theoretical work and the ideas of a reflexive sociology is able to trigger the good questions, more than it claims to offer a complete and self-sufficient sociology of media and inherent here also new media....
Experimental Bell violations with classical, non-entangled optical fields
Gonzales, J.; Sánchez, P.; Barberena, D.; Yugra, Y.; Caballero, R.; De Zela, F.
2018-02-01
We report experiments in which the Bell parameter S that enters the Clauser-Horne-Shimony-Holt inequality: | S| ≤slant 2, attains values | S| > 2. In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η (α ,β ). This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β, which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S. By changing the amount of field correlation, we could cover a range that goes from | S| 2. Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum-classical border.
The S-matrix of superstring field theory
International Nuclear Information System (INIS)
Konopka, Sebastian
2015-01-01
We show that the classical S-matrix calculated from the recently proposed superstring field theories give the correct perturbative S-matrix. In the proof we exploit the fact that the vertices are obtained by a field redefinition in the large Hilbert space. The result extends to include the NS-NS subsector of type II superstring field theory and the recently found equations of motions for the Ramond fields. In addition, our proof implies that the S-matrix obtained from Berkovits’ WZW-like string field theory then agrees with the perturbative S-matrix to all orders.
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
On classical solutions of SU(3) gauge field equations
International Nuclear Information System (INIS)
Chakrabarti, A.
1975-01-01
Static classical solutions of SU(3) gauge field equations are studied. The roles of the O(3) subgroup and of the quadrupole generators are discussed systematically. The general form thus obtained leads, through-out, to a high degree of symmetry in the results. This brings in some simplifying features. An octet of scalar mesons is finally added. Certain classes of exact solutions are given that are singular at the origin. A generalized gauge condition is pointed out. The relation of the general form to known particular cases is discussed [fr
Indian Academy of Sciences (India)
2013-11-11
Nov 11, 2013 ... Polanyi's classic paper, co-authored by Henry Eyring, reproduced in this ... spatial conf guration of the atoms in terms of the energy function of the diatomic .... The present communication deals with the construction of such .... These three contributions are complemented by a fourth term if one takes into.
Enhancing Quantum Discord in Cavity QED by Applying Classical Driving Field
International Nuclear Information System (INIS)
Qian Yi; Xu Jing-Bo
2012-01-01
We investigate the quantum discord dynamics in a cavity quantum electrodynamics system, which consists of two noninteracting two-level atoms driven by independent optical fields and classical fields, and find that the quantum discord vanishes only asymptotically although entanglement disappears suddenly during the time evolution in the absence of classical fields. It is shown that the amount of quantum discord can be increased by adjusting the classical driving fields because the increasing degree of the amount of quantum mutual information is greater than classical correlation by applying the classical driving fields. Finally, the influence of the classical driving field on the fidelity of the system is also examined. (general)
On the general theory of quantized fields
International Nuclear Information System (INIS)
Fredenhagen, K.
1991-10-01
In my lecture I describe the present stage of the general theory of quantized fields on the example of 5 subjects. They are ordered in the direction from large to small distances. The first one is the by now classical problem of the structure of superselection sectors. It involves the behavior of the theory at spacelike infinity and is directly connected with particle statistics and internal symmetries. It has become popular in recent years by the discovery of a lot of nontrivial models in 2d conformal-field theory, by connections to integrable models and critical behavior in statistical mechanics and by the relations to the Jones' theory of subfactors in von Neumann algebras and to the corresponding geometrical objects (braids, knots, 3d manifolds, ...). At large timelike distances the by far most important feature of quantum field theory is the particle structure. This will be the second subject of my lecture. It follows the technically most involved part which is concerned with the behavior at finite distances. Two aspets, nuclearity which emphasizes the finite density of states in phase space, and the modular structure which relies on the infinite number of degrees of freedom present even locally, and their mutual relations will be treated. The next point, involving the structure at infinitesimal distances, is the connection between the Haag-Kastler framework of algebras of local and the framework of Wightman fields. Finally, problems in approaches to quantum gravity will be discussed, as far as they are accessible by the methods of the general theory of quantized fields. (orig.)
International Nuclear Information System (INIS)
Omel'yanchuk, L.V.
1997-01-01
D. Lea classic theory for chromosomal rearrangements formation was modified to account for local interaction of broken chromosome ends. This assumption makes it possible to drastically improve coincidence of the theory and experiment in the case of complex rearrangements
General treatment of quantum and classical spinning particles in external fields
Obukhov, Yuri N.; Silenko, Alexander J.; Teryaev, Oleg V.
2017-11-01
We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial, and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We start from the covariant Dirac equation extended to a spin-1/2 fermion with anomalous magnetic and electric dipole moments and then perform the relativistic Foldy-Wouthuysen transformation. This transformation allows us to obtain the quantum-mechanical equations of motion for the physical operators in the Schrödinger form and to establish the classical limit of relativistic quantum mechanics. The results obtained are then compared to the general classical description of the spinning particle interacting with electromagnetic, inertial and gravitational fields. The complete agreement between the quantum mechanics and the classical theory is proven in the general case. As an application of the results obtained, we consider the dynamics of a spinning particle in a gravitational wave and analyze the prospects of using the magnetic resonance setup to find possible manifestations of the gravitational wave on spin.
Influences on and Limitations of Classical Test Theory Reliability Estimates.
Arnold, Margery E.
It is incorrect to say "the test is reliable" because reliability is a function not only of the test itself, but of many factors. The present paper explains how different factors affect classical reliability estimates such as test-retest, interrater, internal consistency, and equivalent forms coefficients. Furthermore, the limits of classical test…
Modular groups in quantum field theory
International Nuclear Information System (INIS)
Borchers, H.-J.
2000-01-01
The author discusses the connection of Lagrangean quantum field theory, perturbation theory, the Lehmann-Symanzik-Zimmermann theory, Wightman's quantum field theory, the Euclidean quantum field theory, and the Araki-Haag-Kastler theory of local observables with modular groups. In this connection he considers the PCT-theorem, and the tensor product decomposition. (HSI)
Generalized field theory of gravitation
International Nuclear Information System (INIS)
Yilmaz, H.
1976-01-01
It is shown that if, on empirical grounds, one rules out the existence of cosmic fields of Dicke-Brans (scalar) and Will Nordvedt (vector, tensor) type, then the most general experimentally viable and theoretically reasonable theory of gravitation seems to be a LAMBDA-dependent generalization of Einstein and Yilmez theories, which reduces to the former for LAMBDA=0 and to the latter for LAMBDA=1
Pure classical SU(2) Yang-Mills theory with potentials invariant under a U(1) gauge subgroup
International Nuclear Information System (INIS)
Bacry, H.
1978-07-01
The present article is devoted to pure SU(2) classical Yang-Mills theories whose potentials are invariant under a U(1) gauge subgroup. Such potentials are shown to be associated with classical Maxwell-like fields with magnetic sources as 't Hooft's monopole is associated with the Dirac magnetic monopole. Conversely, the authors give Yang-Mills potentials corresponding to some Maxwell-like fields, in particular static magnetic fields with emphasis on those with cylindrical symmetry (including the dipole and other multipoles) and the ephemerons corresponding to an instantaneous magnetic multipole
Infrared behavior of massless field theories
International Nuclear Information System (INIS)
Sapirstein, J.R.
1979-01-01
Typical infrared effects in several gauge field theories with massless particles are investigated in perturbation theory. It is first shown that divergences occurring in individual Feynman graphs arising from integrations over the long-wavelength modes of the fields cancel when the graphs are grouped together in a particular way, in a generalization of the Bloch-Nordsieck treatment of QED. As one of the requirements of finiteness is renormalization of the vector propagator off shell, the charge in these theories is not directly related to classical experiment. In an effort to find the meaning of charge the low-energy theorem is considered. Although in lowest order the graphs reproduce the Thompson limit, it is found that loop corrections are singular in the low-energy limit; a simple definition of the charge is thus precluded. Finally, the behavior of the quark color magnetic moment is treated. An apparent infrared singularity of this moment is shown to be due to an improper use of perturbation theory, and is removed and replaced with a finite, field-dependent moment, by use of Furry picture propagators
Renormalization of topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.; Thompson, G.
1988-11-01
One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs
Topics in conformal field theory
International Nuclear Information System (INIS)
Kiritsis, E.B.
1988-01-01
In this work two major topics in Conformal Field Theory are discussed. First a detailed investigation of N = 2 Superconformal theories is presented. The structure of the representations of the N = 2 superconformal algebras is investigated and the character formulae are calculated. The general structure of N = 2 superconformal theories is elucidated and the operator algebra of the minimal models is derived. The first minimal system is discussed in more detail. Second, applications of the conformal techniques are studied in the Ashkin-Teller model. The c = 1 as well as the c = 1/2 critical lines are discussed in detail
Differential algebras in field theory
International Nuclear Information System (INIS)
Stora, R.
1988-01-01
The applications of differential algebras, as mathematical tools, in field theory are reviewed. The Yang-Mills theories are recalled and the free bosonic string model is treated. Moreover, in the scope of the work, the following topics are discussed: the Faddeev Popov fixed action, in a Feynman like gauge; the structure of local anomalies, including the algebric and the topological theories; the problem of quantizing a degenerate state; and the zero mode problem, in the treatment of the bosonic string conformal gauge. The analysis leads to the conclusion that not much is known about situations where a non involutive distribution is involved
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Using Classical Test Theory and Item Response Theory to Evaluate the LSCI
Schlingman, Wayne M.; Prather, E. E.; Collaboration of Astronomy Teaching Scholars CATS
2011-01-01
Analyzing the data from the recent national study using the Light and Spectroscopy Concept Inventory (LSCI), this project uses both Classical Test Theory (CTT) and Item Response Theory (IRT) to investigate the LSCI itself in order to better understand what it is actually measuring. We use Classical Test Theory to form a framework of results that can be used to evaluate the effectiveness of individual questions at measuring differences in student understanding and provide further insight into the prior results presented from this data set. In the second phase of this research, we use Item Response Theory to form a theoretical model that generates parameters accounting for a student's ability, a question's difficulty, and estimate the level of guessing. The combined results from our investigations using both CTT and IRT are used to better understand the learning that is taking place in classrooms across the country. The analysis will also allow us to evaluate the effectiveness of individual questions and determine whether the item difficulties are appropriately matched to the abilities of the students in our data set. These results may require that some questions be revised, motivating the need for further development of the LSCI. This material is based upon work supported by the National Science Foundation under Grant No. 0715517, a CCLI Phase III Grant for the Collaboration of Astronomy Teaching Scholars (CATS). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Phenomenology of noncommutative field theories
International Nuclear Information System (INIS)
Carone, C D
2006-01-01
Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model
A symplectic framework for field theories
International Nuclear Information System (INIS)
Kijowski, J.; Tulczyjew, W.M.
1979-01-01
These notes are concerned with the formulation of a new conceptual framework for classical field theories. Although the formulation is based on fairly advanced concepts of symplectic geometry these notes cannot be viewed as a reformulation of known structures in more rigorous and elegant torns. Our intention is rather to communicate to theoretical physicists a set of new physical ideas. We have chosen for this purpose the language of local coordinates which is more elementary and more widely known than the abstract language of modern differntial geometry. Our emphasis is directed more to physical intentions than to mathematical vigour. We start with a symplectic analysis of staties. Both discrete and continuous systems are considered on a largely intuitive level. The notion of reciprocity and potentiality of the theory is discussed. Chapter II is a presentation of particle dynamics together with more rigorous definitions of the geometric structure. Lagrangian-Submanifolds and their generating function 3 are defined and the time evolution of particle states is studied. Chapter II form the main part of these notes. Here we describe the construction of canonical momenta and discuss the field dynamics in finite domains of space-time. We also establish the relation between our symplectic framework and the geometric formulation of the calculus of variations of multiple integrals. In the following chapter we give a few examples of field theories selected to illustrate various features of the new approach. A new formulation of the theory of gravity consists of using the affine connection in space-time as the field configuration. In the past section we present an analysis of hydrodynamics within our framework which reveals a formal analogy with electrodynamics. The discovery of potentials for hydrodynamics and the subsequent formulation of a variational principle provides an excellent example for the fruitfulness of the new approach to field theory. A short review of
On the effective field theory of intersecting D3-branes
Abbaspur, Reza
2018-05-01
We study the effective field theory of two intersecting D3-branes with one common dimension along the lines recently proposed in ref. [1]. We introduce a systematic way of deriving the classical effective action to arbitrary orders in perturbation theory. Using a proper renormalization prescription to handle logarithmic divergencies arising at all orders in the perturbation series, we recover the first order renormalization group equation of ref. [1] plus an infinite set of higher order equations. We show the consistency of the higher order equations with the first order one and hence interpret the first order result as an exact RG flow equation in the classical theory.
Gravitation and bilocal field theory
International Nuclear Information System (INIS)
Vollendorf, F.
1975-01-01
The starting point is the conjecture that a field theory of elementary particles can be constructed only in a bilocal version. Thus the 4-dimensional space time has to be replaced by the 8-dimensional manifold R 8 of all ordered pairs of space time events. With special reference to the Schwarzschild metric it is shown that the embedding of the time space into the manifold R 8 yields a description of the gravitational field. (orig.) [de
Vispoel, Walter P; Morris, Carrie A; Kilinc, Murat
2018-03-01
Although widely recognized as a comprehensive framework for representing score reliability, generalizability theory (G-theory), despite its potential benefits, has been used sparingly in reporting of results for measures of individual differences. In this article, we highlight many valuable ways that G-theory can be used to quantify, evaluate, and improve psychometric properties of scores. Our illustrations encompass assessment of overall reliability, percentages of score variation accounted for by individual sources of measurement error, dependability of cut-scores for decision making, estimation of reliability and dependability for changes made to measurement procedures, disattenuation of validity coefficients for measurement error, and linkages of G-theory with classical test theory and structural equation modeling. We also identify computer packages for performing G-theory analyses, most of which can be obtained free of charge, and describe how they compare with regard to data input requirements, ease of use, complexity of designs supported, and output produced. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
String field theory. Algebraic structure, deformation properties and superstrings
International Nuclear Information System (INIS)
Muenster, Korbinian
2013-01-01
This thesis discusses several aspects of string field theory. The first issue is bosonic open-closed string field theory and its associated algebraic structure - the quantum open-closed homotopy algebra. We describe the quantum open-closed homotopy algebra in the framework of homotopy involutive Lie bialgebras, as a morphism from the loop homotopy Lie algebra of closed string to the involutive Lie bialgebra on the Hochschild complex of open strings. The formulation of the classical/quantum open-closed homotopy algebra in terms of a morphism from the closed string algebra to the open string Hochschild complex reveals deformation properties of closed strings on open string field theory. In particular, we show that inequivalent classical open string field theories are parametrized by closed string backgrounds up to gauge transformations. At the quantum level the correspondence is obstructed, but for other realizations such as the topological string, a non-trivial correspondence persists. Furthermore, we proof the decomposition theorem for the loop homotopy Lie algebra of closed string field theory, which implies uniqueness of closed string field theory on a fixed conformal background. Second, the construction of string field theory can be rephrased in terms of operads. In particular, we show that the formulation of string field theory splits into two parts: The first part is based solely on the moduli space of world sheets and ensures that the perturbative string amplitudes are recovered via Feynman rules. The second part requires a choice of background and determines the real string field theory vertices. Each of these parts can be described equivalently as a morphism between appropriate cyclic and modular operads, at the classical and quantum level respectively. The algebraic structure of string field theory is then encoded in the composition of these two morphisms. Finally, we outline the construction of type II superstring field theory. Specific features of the
Dimensional analysis in field theory
International Nuclear Information System (INIS)
Stevenson, P.M.
1981-01-01
Dimensional Transmutation (the breakdown of scale invariance in field theories) is reconciled with the commonsense notions of Dimensional Analysis. This makes possible a discussion of the meaning of the Renormalisation Group equations, completely divorced from the technicalities of renormalisation. As illustrations, I describe some very farmiliar QCD results in these terms
Computers for lattice field theories
International Nuclear Information System (INIS)
Iwasaki, Y.
1994-01-01
Parallel computers dedicated to lattice field theories are reviewed with emphasis on the three recent projects, the Teraflops project in the US, the CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new commercial parallel computers are also discussed. Recent development of semiconductor technologies is briefly surveyed in relation to possible approaches toward Teraflops computers. (orig.)
Topics in quantum field theory
Dams, C.J.F.
2006-01-01
In this PhD-thesis some topics in quantum field theory are considered. The first chapter gives a background to these topics. The second chapter discusses renormalization. In particular it is shown how loop calculations can be performed when using the axial gauge fixing. Fermion creation and
Quantum field theory and parastatistics
International Nuclear Information System (INIS)
Ohnuki, Y.; Kamefuchi, S.
1982-01-01
This book is an introduction to the second quantization of the wave functions of particles obeying the parastatistics. After a general introduction to the canonical quantization for the case of paracommutation relations the nonrelativistic field theory is considered. Thereafter the extension to the relativistic range is discussed. Finally some special problems in connection with parafields are considered. (HSI)
Supercomputers and quantum field theory
International Nuclear Information System (INIS)
Creutz, M.
1985-01-01
A review is given of why recent simulations of lattice gauge theories have resulted in substantial demands from particle theorists for supercomputer time. These calculations have yielded first principle results on non-perturbative aspects of the strong interactions. An algorithm for simulating dynamical quark fields is discussed. 14 refs
Traffic breakdown at a signal: classical theory versus the three-phase theory of city traffic
International Nuclear Information System (INIS)
Kerner, Boris S; Schreckenberg, Michael; Klenov, Sergey L
2014-01-01
Physical reasons for a crucial difference between the results of a three-phase theory developed recently (Kerner 2011 Phys. Rev. E 84 045102(R); 2013 Europhys. Lett. 102 28010; 2014 Physica A 397 76) and the classical theory are explained. Microscopic characteristics of traffic passing a traffic signal during the green signal phase and their dependence on the duration of the green phase have been found. It turns out that a moving synchronized flow pattern (MSP), which occurs in under-saturated traffic at the signal, causes ‘compression’ of traffic flow: the rate of MSP discharge can be considerably larger than the saturation flow rate of the classical traffic theory of city traffic. This leads to a considerably larger rate of traffic passing the signal in comparison with the saturation flow rate. This effect together with traffic behavior at the upstream queue front explains the metastability of under-saturated traffic with respect to a random time-delayed traffic breakdown. (paper)
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Developments in superstring field theory
International Nuclear Information System (INIS)
Green, M.B.
1987-01-01
In this article the structure of superstring theories is outlined. The one-loop quantum superstring gauge anomalies are then described and it is shown that their absence leads to an interesting theory with gauge group SO(32). The one-loop infinities also cancel for this gauge group. The anomaly cancellation can be understood in terms of the low-energy effective supergravity-Yang-Mills field theory, from which it is shown that E 8 x E 8 is an equally good gauge group, which suggests that there should also be an interesting E 8 x E 8 superstring theory. A new type of superstring theory, known as the 'heterotic' string theory, which only describes strings with gauge groups E 8 x E 8 or SO(32) is described. Finally some very exciting prospects for obtaining a sensible description of four-dimensional physics from a ten-dimensional superstring theory with gauge group E 8 x E 8 is outlined. (author)
A critical experimental study of the classical tactile threshold theory
Directory of Open Access Journals (Sweden)
Medina Leonel E
2010-06-01
Full Text Available Abstract Background The tactile sense is being used in a variety of applications involving tactile human-machine interfaces. In a significant number of publications the classical threshold concept plays a central role in modelling and explaining psychophysical experimental results such as in stochastic resonance (SR phenomena. In SR, noise enhances detection of sub-threshold stimuli and the phenomenon is explained stating that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. We designed an experiment to test the validity of the classical vibrotactile threshold. Using a second choice experiment, we show that individuals can order sensorial events below the level known as the classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level contradicting the definition of the classical tactile threshold. Results We performed a three alternative forced choice detection experiment on 6 subjects asking them first and second choices. In each trial, only one of the intervals contained a stimulus and the others contained only noise. According to the classical threshold assumptions, a correct second choice response corresponds to a guess attempt with a statistical frequency of 50%. Results show an average of 67.35% (STD = 1.41% for the second choice response that is not explained by the classical threshold definition. Additionally, for low stimulus amplitudes, second choice correct detection is above chance level for any detectability level. Conclusions Using a second choice experiment, we show that individuals can order sensorial events below the level known as a classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
Zurek, Wojciech Hubert
2018-07-13
The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists-our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification-of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection The pointer states obtained in this way determine what can happen-define events-without appealing to Born's Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance -a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment-through quantum Darwinism This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).
On the Lie symmetry group for classical fields in noncommutative space
Energy Technology Data Exchange (ETDEWEB)
Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)
2011-07-01
Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)
Confusion-limited galaxy fields. II. Classical analyses
International Nuclear Information System (INIS)
Chokshi, A.; Wright, E.L.
1989-01-01
Chokshi and Wright presented a detailed model for simulating angular distribution of galaxy images in fields that extended to very high redshifts. Standard tools are used to analyze these simulated galaxy fields for the Omega(O) = 0 and the Omega(O) = 1 cases in order to test the discriminatory power of these tools. Classical number-magnitude diagrams and surface brightness-color-color diagrams are employed to study crowded galaxy fields. An attempt is made to separate the effects due to stellar evolution in galaxies from those due to the space time geometry. The results show that this discrimination is maximized at near-infrared wavelengths where the stellar photospheres are still visible but stellar evolution effects are less severe than those observed at optical wavelenghts. Rapid evolution of the stars on the asymptotic giant branch is easily recognized in the simulated data for both cosmologies and serves to discriminate between the two extreme values of Omega(O). Measurements of total magnitudes of individual galaxies are not essential for studying light distribution in galaxies as a function of redshift. Calculations for the extragalactic background radiation are carried out using the simulated data, and compared to integrals over the evolutionary models used. 29 refs
Perturbative coherence in field theory
International Nuclear Information System (INIS)
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided they satisfy what they call the 'coherence condition', which is less stringent than the condition for the existence of a Lagrangian. They note that Lagrangian theories are perturbatively coherent, in the sense that they have well defined vertices, and that they satisfy automatically that condition. (G.D.F.) [pt
Einstein's theory of unified fields
Tonnelat, Marie Antoinette
2014-01-01
First published in1966, here is presented a comprehensive overview of one of the most elusive scientific speculations by the pre-eminent genius of the 20th century. The theory is viewed by some scientists with deep suspicion, by others with optimism, but all agree that it represents an extreme challenge. As the author herself affirms, this work is not intended to be a complete treatise or 'didactic exposition' of the theory of unified fields, but rather a tool for further study, both by students and professional physicists. Dealing with all the major areas of research whic
Supersymmetric rings in field theory
International Nuclear Information System (INIS)
Blanco-Pillado, Jose J.; Redi, Michele
2006-01-01
We study the dynamics of BPS string-like objects obtained by lifting monopole and dyon solutions of N = 2 Super-Yang-Mills theory to five dimensions. We present exact traveling wave solutions which preserve half of the supersymmetries. Upon compactification this leads to macroscopic BPS rings in four dimensions in field theory. Due to the fact that the strings effectively move in six dimensions the same procedure can also be used to obtain rings in five dimensions by using the hidden dimension
International Nuclear Information System (INIS)
Akhiezer, A.I.; Shul'ga, N.F.
1991-01-01
The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)
Density dependent hadron field theory
International Nuclear Information System (INIS)
Fuchs, C.; Lenske, H.; Wolter, H.H.
1995-01-01
A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used. Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of 16 O, 40,48 Ca, and 208 Pb are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new ''Coester line'' in the nuclear matter equation of state
"Pathos" Reconsidered from the Perspective of Classical Chinese Rhetorical Theories.
Garrett, Mary M.
1993-01-01
Proposes that cross-cultural rhetorical studies may provide insights into the sources of difficulties with "pathos." Presents an extensive case study that appeals to the emotions in classical Chinese rhetorics. Notes that the presuppositions of these rhetorics highlight the contingent nature of certain fundamental assumptions of many…
How some infinities cause problems in classical physical theories
Atkinson, David; Peijnenburg, Jeanne; Allo, P.; van Kerhove, B.
2014-01-01
In this paper we review a 1992 excursion of Jean Paul Van Bendegem into physics, ‘How Infinities Cause Problems in Classical Physical Theories’, in the light of two later models concerning colliding balls, of Pérez Laraudogoitia and of Alper and Bridger, respectively. We show that Van Bendegem
BQP-completeness of scattering in scalar quantum field theory
Directory of Open Access Journals (Sweden)
Stephen P. Jordan
2018-01-01
Full Text Available Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1 dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.
Variational methods for field theories
Energy Technology Data Exchange (ETDEWEB)
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Dyson quantum field theory. The worldwide known introduction by one of the fathers of the QED
International Nuclear Information System (INIS)
Dyson, Freeman
2014-01-01
The content: The Dirac equation - scattering problems and the Born approximation - the classical and quantum-mechanical field theory - examples of quantized field theories (Maxwell field, Dirac electrons) - scattering problems of free particles (pair annihilation, Moller scattering, Klein-Nishina formula) - general theory of the scattering (Feynman graphs, infrared catastrophe) - scattering on a static potential and experimental results.
Energy momentum tensor and marginal deformations in open string field theory
International Nuclear Information System (INIS)
Sen, Ashoke
2004-01-01
Marginal boundary deformations in a two dimensional conformal field theory correspond to a family of classical solutions of the equations of motion of open string field theory. In this paper we develop a systematic method for relating the parameter labelling the marginal boundary deformation in the conformal field theory to the parameter labelling the classical solution in open string field theory. This is done by first constructing the energy-momentum tensor associated with the classical solution in open string field theory using Noether method, and then comparing this to the answer obtained in the conformal field theory by analysing the boundary state. We also use this method to demonstrate that in open string field theory the tachyon lump solution on a circle of radius larger than one has vanishing pressure along the circle direction, as is expected for a co-dimension one D-brane. (author)
Effective field theory dimensional regularization
International Nuclear Information System (INIS)
Lehmann, Dirk; Prezeau, Gary
2002-01-01
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed
Effective field theory dimensional regularization
Lehmann, Dirk; Prézeau, Gary
2002-01-01
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed.
Theory of field reversed configurations
International Nuclear Information System (INIS)
Steinhauer, L.C.
1990-01-01
This final report surveys the results of work conducted on the theory of field reversed configurations. This project has spanned ten years, beginning in early 1980. During this period, Spectra Technology was one of the leading contributors to the advances in understanding FRC. The report is organized into technical topic areas, FRC formation, equilibrium, stability, and transport. Included as an appendix are papers published in archival journals that were generated in the course of this report. 33 refs
Classical gauge theories on the coadjoint orbits of infinite dimensional groups
International Nuclear Information System (INIS)
Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung
1991-01-01
We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)
Microscopic phenomenon in light of classical and quantum theory
International Nuclear Information System (INIS)
Mandal, C.R.
1999-01-01
Quantum mechanical boundary corrected continuum intermediate state (BCCIS) approximation and classical trajectory Monte Carlo (CTMC) simulation method have been employed to study total charge transfer cross sections in collisions of Be q+ (q = 2-4) and B q+ (q = 3-5) with atomic hydrogen in ground state in the energy range of 30 - 200 keV/amu. Results have been found to be in reasonable agreement with each other. Attempts have been made to find justifications for such resemblance. (author)
The classical theory of the bumpy torus relativistic annulus
International Nuclear Information System (INIS)
Hamasaki, S.; Krall, N.A.; Sperling, J.L.
1983-01-01
The relativistic electron annulus is a critical component of the bumpy torus magnetic fusion concept. An analysis of the annulus is presented in which the ring steady state is determined by the explicit balance of quasi-linear heating and classical losses, i.e. collisions and synchrotron radiation. Both anisotropy and loss-cone effects are included in the formalism. It is demonstrated that a large number of electron cyclotron harmonics, not just the first and second, contribute in an appreciable way to annulus steady state and power balance. Without a loss cone, the analysis reproduces the relativistic passing electron population observed in bumpy tori on confined drift surfaces near the centre of the bumpy torus cross-section. Loss-cone effects permit an annulus population with large perpendicular pressure to exist. It is shown that the balance between quasi-linear heating and the classical losses cannot account for the experimental scaling of bumpy torus annulus temperature; therefore, processes not included in the classical ring power balance model must contribute in a non-trivial way to observed annulus properties. (author)
Group field theory with noncommutative metric variables.
Baratin, Aristide; Oriti, Daniele
2010-11-26
We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.
Structural aspects of quantum field theory and noncommutative geometry
Grensing, Gerhard
2013-01-01
This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...
The method of finite-gap integration in classical and semi-classical string theory
International Nuclear Information System (INIS)
Vicedo, Benoit
2011-01-01
In view of proving the AdS/CFT correspondence one day, a deeper understanding of string theory on certain curved backgrounds such as AdS 5 x S 5 is required. In this review we make a step in this direction by focusing on RxS 3 . It was discovered in recent years that string theory on AdS 5 x S 5 admits a Lax formulation. However, the complete statement of integrability requires not only the existence of a Lax formulation but also that the resulting integrals of motion are in pairwise involution. This idea is central to the first part of this review. Exploiting this integrability we apply algebro-geometric methods to string theory on RxS 3 and obtain the general finite-gap solution. The construction is based on an invariant algebraic curve previously found in the AdS 5 x S 5 case. However, encoding the dynamics of the solution requires specification of additional marked points. By restricting the symplectic structure of the string to these algebro-geometric data we derive the action-angle variables of the system. We then perform a first-principle semiclassical quantization of string theory on RxS 3 as a toy model for strings on AdS 5 x S 5 . The result is exactly what one expects from the dual gauge theory perspective, namely the underlying algebraic curve discretizes in a natural way. We also derive a general formula for the fluctuation energies around the generic finite-gap solution. The ideas used can be generalized to AdS 5 x S 5 . (review)
Braided quantum field theories and their symmetries
International Nuclear Information System (INIS)
Sasai, Yuya; Sasakura, Naoki
2007-01-01
Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided quantum field theories that are required for the relations to hold. As concrete examples, we apply our analysis to the Poincare symmetries of two examples of noncommutative field theories. One is the effective quantum field theory of three-dimensional quantum gravity coupled to spinless particles formulated by Freidel and Livine, and the other is noncommutative field theory on the Moyal plane. We also comment on quantum field theory in κ-Minkowski spacetime. (author)
Introduction to conformal field theory. With applications to string theory
International Nuclear Information System (INIS)
Blumenhagen, Ralph; Plauschinn, Erik
2009-01-01
Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields. (orig.)
(Non-)decoupled supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Pietro, Lorenzo Di [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel); Dine, Michael [Santa Cruz Institute for Particle Physics and Department of Physics,Santa Cruz CA 95064 (United States); Komargodski, Zohar [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel)
2014-04-10
We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS{sub 4} Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)
(Non-)decoupled supersymmetric field theories
International Nuclear Information System (INIS)
Pietro, Lorenzo Di; Dine, Michael; Komargodski, Zohar
2014-01-01
We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS 4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)
International Nuclear Information System (INIS)
French, Doug; Huang Zun; Pao, H.-Y.; Jovanovic, Igor
2009-01-01
A quantum phase amplifier operated in the spatial domain can improve the signal-to-noise ratio in imaging beyond the classical limit. The scaling of the signal-to-noise ratio with the gain of the quantum phase amplifier is derived from classical information theory
String field theory-inspired algebraic structures in gauge theories
International Nuclear Information System (INIS)
Zeitlin, Anton M.
2009-01-01
We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.
On the stability of the asymptotically free scalar field theories
Energy Technology Data Exchange (ETDEWEB)
Shalaby, A M. [Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha (Qatar); Physics Department, Faculty of Science, Mansoura University, Egypt. amshalab@qu.edu.qa (Egypt)
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Cosmological viability of theories with massive spin-2 fields
Energy Technology Data Exchange (ETDEWEB)
Koennig, Frank
2017-03-30
Theories of spin-2 fields take on a particular role in modern physics. They do not only describe the mediation of gravity, the only theory of fundamental interactions of which no quantum field theoretical description exists, it furthermore was thought that they necessarily predict massless gauge bosons. Just recently, a consistent theory of a massive graviton was constructed and, subsequently, generalized to a bimetric theory of two interacting spin-2 fields. This thesis studies both the viability and consequences at cosmological scales in massive gravity as well as bimetric theories. We show that all consistent models that are free of gradient and ghost instabilities behave like the cosmological standard model, LCDM. In addition, we construct a new theory of massive gravity which is stable at both classical background and quantum level, even though it suffers from the Boulware-Deser ghost.
Comparison of classical and modern theories of longitudinal wave propagation in elastic rods
CSIR Research Space (South Africa)
Shatalov, M
2009-07-01
Full Text Available are constructed for the classical, Rayleigh, Bishop, and Mindlin-Herrmann models in which the general solutions of the problem are obtained. The principles of construction of the multimode theories, corresponding equations and orthogonality conditions...
Classical Belief Conditioning and its Generalization to DSm Theory
Czech Academy of Sciences Publication Activity Database
Daniel, Milan
2008-01-01
Roč. 2, č. 4 (2008), s. 267-279 ISSN 1752-8917 R&D Projects: GA AV ČR 1ET100300419 Institutional research plan: CEZ:AV0Z10300504 Keywords : belief functions * Dempster-Shafer theory * belief conditioning * DSm theory * overlapping elements * hyper-power set * DSm model Subject RIV: BA - General Mathematics http://www.worldacademicunion.com/journal/jus/jusVol02No4paper04.pdf
Classical particles with spin in electromagnetic and gravitational fields
International Nuclear Information System (INIS)
Amorim, R.M. de.
1977-02-01
Following a review of several problems connected with classical particles with intrinsic angular momentum are reproduced the Frenkel equations (with the condition S sup(μν)U sub(ν)=0) by means of a holonomic variational principle, and have related them to Bargann, Michel and Tededgie equations. The treatment is then generalized to the case in wich S sup(μν)U sub(ν)=0 and the resulting equation coincide in the linearized limit with those obtained by Suttorp and de Groot. Also, by using variational principles, the generalizations to Frenkel equations are obtained, as well as to those of Suttorp and de Groot when electromagnetic and gravitational interactions are considered. Finally, those equations are analysed according to a scheme proposed by Oliveira and Tiommo where the gravitational interactions are described by gravielectric and gravimagnetic fields. The analogies in these equations of motion between the gravitational and eletromagnetic interactions, in the case in which the particle has a giromagnetic factor g=1, are shown. The last results complete a previous study by wald. (Author) [pt
Classical optics in generalized Maxwell Chern-Simons theory
International Nuclear Information System (INIS)
Burgess, M.; Leinaas, J.M.; Loevvik, O.M.
1993-03-01
The authors consider the propagation of electromagnetic waves in a two-dimensional polarizable medium endowed with Chern-Simons terms. The dispersion relation (refractive index) of the waves is computed and the existence of linear birefringence and anomalous dispersion is shown. When absorption is taken into account, the classic signature of a Voigt effect is found. In the case where linearly-polarized, three-dimensional waves pass through a two-dimensional plane, it is shown that there is optical activity, and the analogue of Verdet's constant is computed. 19 refs., 2 figs
Renormalons in effective field theories
International Nuclear Information System (INIS)
Luke, M.; Manohar, A.V.; Savage, M.J.
1995-01-01
We investigate the high-order behavior of perturbative matching conditions in effective field theories. These series are typically badly divergent, and are not Borel summable due to infrared and ultraviolet renormalons which introduce ambiguities in defining the sum of the series. We argue that, when treated consistently, there is no physical significance to these ambiguities. Although nonperturbative matrix elements and matching conditions are in general ambiguous, the ambiguity in any physical observable is always higher order in 1/M than the theory has been defined. We discuss the implications for the recently noticed infrared renormalon in the pole mass of a heavy quark. We show that a ratio of form factors in exclusive Λ b decays (which is related to the pole mass) is free from renormalon ambiguities regardless of the mass used as the expansion parameter of heavy quark effective theory. The renormalon ambiguities also cancel in inclusive heavy hadron decays. Finally, we demonstrate the cancellation of renormalons in a four-Fermi effective theory obtained by integrating out a heavy colored scalar
All the mathematics in the world: logical validity and classical set theory
Directory of Open Access Journals (Sweden)
David Charles McCarty
2017-12-01
Full Text Available A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.
Asymptotic behaviour in field theory
Energy Technology Data Exchange (ETDEWEB)
Banerjee, H.
1980-07-01
Asymptotic behaviour in field theory has been studied and the anomalies are pointed out in two specific cases, (i) the infrared and fixed angle high energy behaviour in the non-trivial case of the 'box' amplitude in a scalar-scalar theory and (ii) high energy behaviour of a sixth order Yang-Mills diagram. A set of rules are presented for writing down the precise leading infrared behaviour of an arbitrary generalised ladder diagram (GLD) in QED. These rules are the final result of a detailed analysis of the relevant amplitudes in the Feynman parameter space. The connection between the infrared and fixed angle high energy limits of generalised ladder diagrams is explained. It is argued that the same set of rules yield the fixed angle high energy limit.
Inverse bootstrapping conformal field theories
Li, Wenliang
2018-01-01
We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new method, we reverse the logic and interpret manifestly crossing-symmetric functions as generating functions of conformal data. Physical CFTs can be obtained by scanning the space of crossing-symmetric functions. By truncating the fusion rules, we are able to concentrate on the low-lying operators and derive some approximate relations for their conformal data. It turns out that the free scalar theory, the 2d minimal model CFTs, the ϕ 4 Wilson-Fisher CFT, the Lee-Yang CFTs and the Ising CFTs are consistent with the universal relations from the minimal fusion rule ϕ 1 × ϕ 1 = I + ϕ 2 + T , where ϕ 1 , ϕ 2 are scalar operators, I is the identity operator and T is the stress tensor.
Orthogonal polynomials on the unit circle part 1 classical theory
2009-01-01
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (SzegÅ‘'s theorems), limit theorems for the density of the zeros of orthogonal po
THE CONCEPT OF INTERNATIONAL TRADE AND MAIN CLASSIC THEORIES
Directory of Open Access Journals (Sweden)
Elena Ramona TERZEA
2016-07-01
Full Text Available Taking into account the major impact that international trade has on the economy and on the people’s lives, and considering its effects on the economic growth, the foreign commerce has to be well understood so that the commercial policies have to be well elaborated, implemented and followed. The theories of international trade are extremely important in order to determine the flows, but especially in the anticipation of the evolution of the forces that influences its dymanic. The theories regarding the foreign trade are used also by the big companies, by their managers, in their attempt to identify the most advantageous strategies of internationalizations, on the most promising markets.
Restrictions on Possible Forms of Classical Matter Fields Carrying no Energy
International Nuclear Information System (INIS)
Sokolowski, L.M.
2004-01-01
It is postulated in general relativity that the matter energy-momentum tensor vanishes if and only if all the matter fields vanish. In classical Lagrangian field theory the energy and momentum density are described by the variational (symmetric) energy-momentum tensor (named the stress tensor) and a priori it might occur that for some systems the tensor is identically to zero for all field configurations whereas evolution of the system is subject to deterministic Lagrange equations of motion. Such a system would not generate its own gravitational field. To check if these systems can exist in the framework of classical field theory we find a relationship between the stress tensor and the Euler operator (i.e. the Lagrange field equations). We prove that if a system of interacting scalar fields (the number of fields cannot exceed the spacetime dimension d) or a single vector field (in spacetimes with d even) has the stress tensor such that its divergence is identically zero (i.e. ''on and of shell''), then the Lagrange equations of motion hold identically too. These systems have then no propagation equations at all and should be regarded as unphysical. Thus nontrivial field equations require the stress tensor be nontrivial too. This relationship between vanishing (of divergence) of the stress tensor and of the Euler operator breaks down if the number of fields is greater than d. We show on concrete examples that a system of n > d interacting scalars or two interacting vector fields can have the stress tensor equal identically to zero while their propagation equations are nontrivial. This means that non-self-gravitating (and yet detectable) field systems are in principle admissible. Their equations of motion are, however, in some sense degenerate. We also show, that for a system of arbitrary number of interacting scalar fields or for a single vector field (in some specific spacetimes in the latter case), if the stress tensor is not identically zero, then it cannot
The utility of quantum field theory
International Nuclear Information System (INIS)
Dine, Michael
2001-01-01
This talk surveys a broad range of applications of quantum field theory, as well as some recent developments. The stress is on the notion of effective field theories. Topics include implications of neutrino mass and a possible small value of sin(2β), supersymmetric extensions of the standard model, the use of field theory to understand fundamental issues in string theory (the problem of multiple ground states and the question: does string theory predict low energy supersymmetry), and the use of string theory to solve problems in field theory. Also considered are a new type of field theory, and indications from black hole physics and the cosmological constant problem that effective field theories may not completely describe theories of gravity. (author)
Classical hair in string theory. II. Explicit calculations
International Nuclear Information System (INIS)
Larsen, F.
1997-01-01
For pt.I see ibid., vol.475, p.627-44, 1996. After emphasizing the importance of obtaining a space-time understanding of black hole entropy, we further elaborate our program to identify the degrees of freedom of black holes with classical space-time degrees of freedom. The Cvetic-Youm dyonic black holes are discussed in some detail as an example. In this example hair degrees of freedom transforming as an effective string can be identified explicitly. We discuss issues concerning charge quantization, identification of winding, and tension renormalization that arise in counting the associated degrees of freedom. The possibility of other forms of hair in this example, and the prospects for making contact with D-brane ideas, are briefly considered. (orig.)
Classical theory of thermal radiation from a solid.
Guo, Wei
2016-06-01
In this work, a solid at a finite temperature is modeled as an ensemble of identical atoms, each of which moves around a lattice site inside an isotropic harmonic potential. The motion of one such atom is studied first. It is found that the atom moves like a time-dependent current density and, thus, can emit electromagnetic radiation. Since all the atoms are identical, they can radiate, too. The resultant radiation from the atoms is the familiar thermal radiation from the solid. After its general expression is obtained, the intensity of the thermal radiation is discussed for its properties, and specifically calculated in the low-temperature limit. Both atomic motion and radiation are formulated in the classical domain.
Foundations of the classical theory of partial differential equations
Egorov, Yu V
1998-01-01
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Coura...
Thermal and viscous effects on sound waves: revised classical theory.
Davis, Anthony M J; Brenner, Howard
2012-11-01
In this paper the recently developed, bi-velocity model of fluid mechanics based on the principles of linear irreversible thermodynamics (LIT) is applied to sound propagation in gases taking account of first-order thermal and viscous dissipation effects. The results are compared and contrasted with the classical Navier-Stokes-Fourier results of Pierce for this same situation cited in his textbook. Comparisons are also made with the recent analyses of Dadzie and Reese, whose molecularly based sound propagation calculations furnish results virtually identical with the purely macroscopic LIT-based bi-velocity results below, as well as being well-supported by experimental data. Illustrative dissipative sound propagation examples involving application of the bi-velocity model to several elementary situations are also provided, showing the disjoint entropy mode and the additional, evanescent viscous mode.
Progress in the application of classical S-matrix theory to inelastic collision processes
International Nuclear Information System (INIS)
McCurdy, C.W.; Miller, W.H.
1980-01-01
Methods are described which effectively solve two of the technical difficulties associated with applying classical S-matrix theory to inelastic/reactive scattering. Specifically, it is shown that rather standard numerical methods can be used to solve the ''root search'' problem (i.e., the nonlinear boundary value problem necessary to impose semiclassical quantum conditions at the beginning and the end of the classical trajectories) and also how complex classical trajectories, which are necessary to describe classically forbidden (i.e., tunneling) processes, can be computed in a numerically stable way. Application is made to vibrational relaxation of H 2 by collision with He (within the helicity conserving approximation). The only remaining problem with regard to applying classical S-matrix theory to complex collision processes has to do with the availability of multidimensional uniform asymptotic formulas for interpolating the ''primitive'' semiclassical expressions between their various regions of validity
Some global charges in classical Yang-Mills theory
International Nuclear Information System (INIS)
Chrus'ciel, P.T.; Kondracki, W.
1987-01-01
Three classes of boundary conditions allowing the definition of a global field strength (''global color'') are presented. A definition of global color of the sources and of the Yang-Mills field is proposed. Some exact solutions of Yang-Mills equations with point sources and with ''topologically nontrivial electric color'' are presented
Topics in low-dimensional field theory
International Nuclear Information System (INIS)
Crescimanno, M.J.
1991-01-01
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density
Fedosov quantization and perturbative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Collini, Giovanni
2016-12-12
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (''phase space''). His algorithm gives a non-commutative, but associative, product (a so-called ''star-product'') between smooth phase space functions parameterized by Planck's constant ℎ, which is treated as a deformation parameter. In the limit as ℎ goes to zero, the star product commutator goes to ℎ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, a generalization of Fedosov's method is developed which applies to the infinite-dimensional symplectic ''manifolds'' that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of the method to more standard perturbative quantization schemes in quantum field theory.
Field theory of the spinning electron: Internal motions
Salesi, Giovanni; Recami, Erasmo
1996-01-01
We present here a field theory of the spinning electron, by writing down a new equation for the 4-velocity field v^mu (different from that of Dirac theory), which allows a classically intelligible description of the electron. Moreover, we make explicit the noticeable kinematical properties of such velocity field (which also result different from the ordinary ones). At last, we analyze the internal zitterbewegung (zbw) motions, for both time-like and light-like speeds. We adopt in this paper t...
The Global Approach to Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Fulling, S A [Texas A and M University (United States)
2006-05-21
Parts I and II develop the basic classical and quantum kinematics of fields and other dynamical systems. The presentation is conducted in the utmost generality, allowing for dynamical quantities that may be anticommuting (supernumbers) and theories subject to the most general possible gauge symmetry. The basic ingredients are action functionals and the Peierls bracket, a manifestly covariant replacement for the Poisson bracket and equal-time commutation relations. For DeWitt the logical progression is Peierls bracket {yields} Schwinger action principle {yields} Feynman functional integral although he points out that the historical development was in the opposite order. It must be pointed out that the Peierls-Schwinger-DeWitt approach, despite some advantages over initial-value formulations, has some troubles of its own. In particular, it has never completely escaped from the arena of scattering theory, the paradigm of conventional particle physics. One is naturally led to study matrix elements between an 'in-vacuum' and an 'out-vacuum' though such concepts are murky in situations, such as big bangs and black holes, where the ambient geometry is not asymptotically static in the far past and future. The newest material in the treatise appears in two chapters in part II devoted to the interpretation of quantum theory, incorporating some unpublished work of David Deutsch on the meaning of probability in physics. Parts III through V apply the formalism in depth to successively more difficult classes of systems: quantum mechanics, linear (free) fields, and interacting fields. DeWitt's characteristic tools of effective actions, heat kernels, and ghost fields are developed. Chapters 26 and 31 outline new approaches developed in collaboration with DeWitt's recent students C Molina-Paris and C Y Wang, respectively. The most of parts VI and VII consist of special topics, such as anomalies, particle creation by external fields, Unruh acceleration
The Global Approach to Quantum Field Theory
International Nuclear Information System (INIS)
Fulling, S A
2006-01-01
Parts I and II develop the basic classical and quantum kinematics of fields and other dynamical systems. The presentation is conducted in the utmost generality, allowing for dynamical quantities that may be anticommuting (supernumbers) and theories subject to the most general possible gauge symmetry. The basic ingredients are action functionals and the Peierls bracket, a manifestly covariant replacement for the Poisson bracket and equal-time commutation relations. For DeWitt the logical progression is Peierls bracket → Schwinger action principle → Feynman functional integral although he points out that the historical development was in the opposite order. It must be pointed out that the Peierls-Schwinger-DeWitt approach, despite some advantages over initial-value formulations, has some troubles of its own. In particular, it has never completely escaped from the arena of scattering theory, the paradigm of conventional particle physics. One is naturally led to study matrix elements between an 'in-vacuum' and an 'out-vacuum' though such concepts are murky in situations, such as big bangs and black holes, where the ambient geometry is not asymptotically static in the far past and future. The newest material in the treatise appears in two chapters in part II devoted to the interpretation of quantum theory, incorporating some unpublished work of David Deutsch on the meaning of probability in physics. Parts III through V apply the formalism in depth to successively more difficult classes of systems: quantum mechanics, linear (free) fields, and interacting fields. DeWitt's characteristic tools of effective actions, heat kernels, and ghost fields are developed. Chapters 26 and 31 outline new approaches developed in collaboration with DeWitt's recent students C Molina-Paris and C Y Wang, respectively. The most of parts VI and VII consist of special topics, such as anomalies, particle creation by external fields, Unruh acceleration temperature, black holes, and
Generalized Field Theory and Kasner universe
International Nuclear Information System (INIS)
Klotz, A.H.
1986-01-01
It is shown that the only Kasner-like solution of the Generalized Field Theory field equations with a nonzero electromagnetic field corresponds to an empty field geometry of the space-time. In this case, the electromagnetic field tensors of the theory coincide as could be expected from general considerations. 6 refs. (author)
Classical scattering cross section in sputtering transport theory
International Nuclear Information System (INIS)
Zhang Zhulin
2002-01-01
For Lindhard scaling interaction potential scattering commonly used in sputtering theory, the authors analyzed the great difference between Sigmund's single power and the double power cross sections calculated. The double power cross sections can give a much better approximation to the Born-Mayer scattering in the low energy region (m∼0.1). In particular, to solve the transport equations by K r -C potential interaction given by Urbassek few years ago, only the double power cross sections (m∼0.1) can yield better approximate results for the number of recoils. Therefore, the Sigmund's single power cross section might be replaced by the double power cross sections in low energy collision cascade theory
Generic f(R) theories and classicality of their scalarons
Energy Technology Data Exchange (ETDEWEB)
Gannouji, Radouane [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Sami, M., E-mail: samijamia@gmail.com [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Thongkool, I. [Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad-211019 (India)
2012-09-19
We study quantum stability bound on the mass of scalaron in generic theories of f(R) gravity. We show that in these scenarios, the scalaron mass increases faster with local density of the environment than one-loop quantum correction to it thereby leading to violation of quantum bound on the chameleon mass. The introduction of quadratic curvature corrections in the action are shown to stabilize the model.
An empirical comparison of Item Response Theory and Classical Test Theory
Directory of Open Access Journals (Sweden)
Špela Progar
2008-11-01
Full Text Available Based on nonlinear models between the measured latent variable and the item response, item response theory (IRT enables independent estimation of item and person parameters and local estimation of measurement error. These properties of IRT are also the main theoretical advantages of IRT over classical test theory (CTT. Empirical evidence, however, often failed to discover consistent differences between IRT and CTT parameters and between invariance measures of CTT and IRT parameter estimates. In this empirical study a real data set from the Third International Mathematics and Science Study (TIMSS 1995 was used to address the following questions: (1 How comparable are CTT and IRT based item and person parameters? (2 How invariant are CTT and IRT based item parameters across different participant groups? (3 How invariant are CTT and IRT based item and person parameters across different item sets? The findings indicate that the CTT and the IRT item/person parameters are very comparable, that the CTT and the IRT item parameters show similar invariance property when estimated across different groups of participants, that the IRT person parameters are more invariant across different item sets, and that the CTT item parameters are at least as much invariant in different item sets as the IRT item parameters. The results furthermore demonstrate that, with regards to the invariance property, IRT item/person parameters are in general empirically superior to CTT parameters, but only if the appropriate IRT model is used for modelling the data.
L{sub ∞} algebras and field theory
Energy Technology Data Exchange (ETDEWEB)
Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY (United States); Zwiebach, Barton [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)
2017-03-15
We review and develop the general properties of L{sub ∞} algebras focusing on the gauge structure of the associated field theories. Motivated by the L{sub ∞} homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L{sub ∞} structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L{sub ∞} algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L{sub ∞} algebra for the interacting theory. The analysis suggests that L{sub ∞} algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A Wigner quasi-distribution function for charged particles in classical electromagnetic fields
International Nuclear Information System (INIS)
Levanda, M.; Fleurov, V.
2001-01-01
A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and canonical momenta in the Wigner representation. Gauge-invariant quantum analogs of Hamilton-Jacobi and Boltzmann kinetic equations are formulated for arbitrary classical electromagnetic fields in terms of the 'slashed' derivatives and momenta, introduced for this purpose. The kinetic meaning of these slashed quantities is discussed. We introduce gauge-invariant conditional moments and use them to derive a kinetic momentum continuity equation. This equation provides us with a hydrodynamic representation for quantum transport processes and a definition of the 'collision force'. The hydrodynamic equation is applied for the rotation part of the electron motion. The theory is illustrated by its application in three examples: Wigner quasi-distribution function and equations for an electron in a magnetic field and harmonic potential; Wigner quasi-distribution function for a charged particle in periodic systems using the kq representation; two Wigner quasi-distribution functions for heavy-mass polaron in an electric field
Quantum Field Theory in (0 + 1) Dimensions
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Relativistic quantum mechanics and introduction to field theory
Energy Technology Data Exchange (ETDEWEB)
Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-12-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.
Relativistic quantum mechanics and introduction to field theory
International Nuclear Information System (INIS)
Yndurain, F.J.
1996-01-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources
Nonrelativistic Conformed Symmetry in 2 + 1 Dimensional Field Theory.
Bergman, Oren
This thesis is devoted to the study of conformal invariance and its breaking in non-relativistic field theories. It is a well known feature of relativistic field theory that theories which are conformally invariant at the classical level can acquire a conformal anomaly upon quantization and renormalization. The anomaly appears through the introduction of an arbitrary, but dimensionful, renormalization scale. One does not usually associate the concepts of renormalization and anomaly with nonrelativistic quantum mechanics, but there are a few examples where these concepts are useful. The most well known case is the two-dimensional delta -function potential. In two dimensions the delta-function scales like the kinetic term of the Hamiltonian, and therefore the problem is classically conformally invariant. Another example of classical conformal invariance is the famous Aharonov-Bohm (AB) problem. In that case each partial wave sees a 1/r^2 potential. We use the second quantized formulation of these problems, namely the nonrelativistic field theories, to compute Green's functions and derive the conformal anomaly. In the case of the AB problem we also solve an old puzzle, namely how to reproduce the result of Aharonov and Bohm in perturbation theory. The thesis is organized in the following manner. Chapter 1 is an introduction to nonrelativistic field theory, nonrelativistic conformal invariance, contact interactions and the AB problem. In Chapter 2 we discuss nonrelativistic scalar field theory, and how its quantization produces the anomaly. Chapter 3 is devoted to the AB problem, and the resolution of the perturbation puzzle. In Chapter 4 we generalize the discussion of Chapter 3 to particles carrying nonabelian charges. The structure of the nonabelian theory is much richer, and deserves a separate discussion. We also comment on the issues of forward scattering and single -valuedness of wavefunctions, which are important for Chapter 3 as well. (Copies available
Microscopic aspects of wetting using classical density functional theory
Yatsyshin, P.; Durán-Olivencia, M.-A.; Kalliadasis, S.
2018-07-01
Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid–fluid and fluid–substrate intermolecular interactions brings about an entire ‘zoo’ of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid–gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid–gas interface is already highly complex and non-trivial.
Semi-classical theory of fluctuations in nuclear matter
International Nuclear Information System (INIS)
Benhassine, B.
1994-01-01
At intermediate energies the heavy ion collisions can be studied within the framework of a semi-classical approach based on the Vlasov-Uehling-Uhlenbeck (VUU) equation. Such an approach reduces the N-body problem to its description in terms of the one-body distribution function and constitutes the basis of several successful simulation models. Our aim in this work is to extend these average approaches to treat fluctuations. Within the framework of a linear approximation, we derived a Fokker-Planck transport equation in the one-body phase space. When it is reduced to its first moments, one recovers the VUU equation for the average dynamics together with the time evolution equation for the correlations. The collective transport coefficients are then obtained by projection on the one-body collective space. Independently, using a projection method introduced by Van Kampen, based on the constants of motion, we deduce the stationary expressions for the covariance matrix in phase space. We extract then, the equilibrium dispersions of one-body observables in a homogeneous case and in a spherical symmetric one. These results are compared with two types of simulation models in a relaxation time approximation. In the first one which is of Lagrangian type, the collective transport coefficients are directly extracted from the simulation and consequently the numerical fluctuations are washed out. The second model, due to its Eulerian character, allows us to make a microscopical comparison. (author)
Opportunizing: A classic grounded theory study on business and management
Directory of Open Access Journals (Sweden)
Ólavur Christiansen
2006-11-01
Full Text Available Opportunizing emerged as the core variable of this classic GT study on business and management. Opportunizing is the recurrent main concern that businesses have to continually resolve, and it explains how companies recurrently create, identify, seize or exploit situations to maintain their growth or survival. Opportunizing is the recurrent creation and re-creation of opportunities in business. Opportunizing is basically what business managers do and do all the time. The problematic nature of opportunizing is resolved by a core social process ofopportunizing and its attached sub-processes that account for change over time and for the variations of the problematic nature of its resolution.Opportunizing has five main facets. These are conditional befriending (confidence building & modifying behavior,prospecting (e.g. information gaining, weighing up (information appraisal & decision-making, moment capturing (quick intervention for seizing strategic opportunities, andconfiguration matching (adjusting the business organization to abet the other activities of opportunizing.On a more abstract level, opportunizing has three more organizational facets: the physically boundary-less, the valuehierarchical, and the physically bounded. The first of these called perpetual opportunizing. This emerges from the conjunction of conditional befriending and prospecting. The second facet is called triggering opportunizing. It arises from the coming together of weighing up and moment capturing. The final facet is called spasmodic opportunizing. This happens when moment capturing and configuration matching unite.
Hamiltonian Anomalies from Extended Field Theories
Monnier, Samuel
2015-09-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
Quantum field theory a tourist guide for mathematicians
Folland, Gerald B
2008-01-01
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theor...
The contrasting roles of Planck's constant in classical and quantum theories
Boyer, Timothy H.
2018-04-01
We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.
Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)
International Nuclear Information System (INIS)
Shen Jianmin; Sheng Zhengmao; Wang Zhonghua
1992-02-01
We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs
International Nuclear Information System (INIS)
Cheng Hung; Tsai Ercheng
1986-01-01
We give a correspondence formula which equates transition amplitudes in a quantum gauge field theory without ghost fields to those in a quantum theory with the gauge fields covariantly quantized and coupled to ghost fields. (orig.)
Longitudinal vibration of isotropic solid rods: from classical to modern theories
CSIR Research Space (South Africa)
Shatalov, M
2011-12-01
Full Text Available Vibration of Isotropic Solid Rods: From Classical to Modern Theories Michael Shatalov1,2, Julian Marais2, Igor Fedotov2 and Michel Djouosseu Tenkam2 1Council for Scientific and Industrial Research 2Tshwane University of Technology South Africa 1...). The classical approximate theory of longitudinal vibration of rods was developed during the 18th century by J. D?Alembert, D. Bernoulli, L. Euler and J. Lagrange. This theory is based on the analysis of the one dimensional wave equation and is applicable...
Gaussian processes and constructive scalar field theory
International Nuclear Information System (INIS)
Benfatto, G.; Nicolo, F.
1981-01-01
The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)
Dirac's equation and the nature of quantum field theory
International Nuclear Information System (INIS)
Plotnitsky, Arkady
2012-01-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Features of finite quantum field theories
International Nuclear Information System (INIS)
Boehm, M.; Denner, A.
1987-01-01
We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)
Effective Field Theory on Manifolds with Boundary
Albert, Benjamin I.
In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Differential pseudoconnections and field theories
International Nuclear Information System (INIS)
Modugno, Marco; Ragionieri, Rodolfo; Stefani, Gianna
1981-01-01
Several general field theories have been successful in describing fundamental physical fields by a unique schema. Our purpose is to present the first step of an attempt based on differential pseudoconnections on jet bundles. In this paper we are dealing with the essential elements of such an approach and with the testing of a certain number of important examples. We define a 'differential pseudoconnection of order k' on a bundle p:E→M as a translation morphism on the affine bundle. Such concept is a generalization of usual connections. Then we study in the framework of jet spaces several important differential operators used in physics. In this context an interest arises naturally for the second order affine differential equations, called 'special'. Particular cases of special equations are both the geodesics equation (an ordinary equation) and any Kind of Laplace equation (a partial equation) even modified by the addition of physical terms. So special equations are candidate to fit a lot of fundamental physical fields
Classical and modern numerical analysis theory, methods and practice
Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan
2009-01-01
Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...
Quantum field theory of universe
International Nuclear Information System (INIS)
Hosoya, Akio; Morikawa, Masahiro.
1988-08-01
As is well-known, the wave function of universe dictated by the Wheeler-DeWitt equation has a difficulty in its probabilistic interpretation. In order to overcome this difficulty, we explore a theoretical possibility of the second quantization of universe, following the same passage historically taken for the Klein-Gordon particles and the Nambu-Goto strings. It turns out that multiple production of universes is an inevitable consequence even if the initial state is nothing. The problematical interpretation of wave function of universe is circumvented by introducing an internal comoving model detector, which is an analogue of the DeWitt-Unruh detector in the quantum field theory in curved space-time. (author)
Quantum Field Theory A Modern Perspective
Parameswaran Nair, V
2005-01-01
Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...
N=1 field theory duality from M theory
International Nuclear Information System (INIS)
Schmaltz, M.; Sundrum, R.
1998-01-01
We investigate Seiberg close-quote s N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in type IIA string theory is given an elegant derivation from M theory. copyright 1998 The American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Latyshev, A. V., E-mail: avlatyshev@mail.ru; Yushkanov, A. A. [Moscow State Regional University (Russian Federation)
2015-09-15
A distribution function for collisionless plasma is derived from the Vlasov kinetic equation in the quadratic approximation with respect to the electromagnetic field. Formulas for calculation of the electric current at an arbitrary temperature (arbitrary degree of degeneration of the electron gas) are deduced. The case of small wavenumbers is considered. It is shown that nonlinearity leads to the generation of an electric current directed along the wave vector. This longitudinal current is orthogonal to the classical transverse current, well known in the linear theory. A distribution function for collisionless quantum plasma is derived from the kinetic equation with the Wigner integral in the quadratic approximation with respect to the vector potential. Formulas for calculation of the electric current at an arbitrary temperature are deduced. The case of small wavenumbers is considered. It is shown that, at small values of the wavenumber, the value of the longitudinal current for quantum plasma coincides with that for classical plasma. The dimensionless currents in quantum and classical plasmas are compared graphically.
Methods of geometric function theory in classical and modern problems for polynomials
International Nuclear Information System (INIS)
Dubinin, Vladimir N
2012-01-01
This paper gives a survey of classical and modern theorems on polynomials, proved using methods of geometric function theory. Most of the paper is devoted to results of the author and his students, established by applying majorization principles for holomorphic functions, the theory of univalent functions, the theory of capacities, and symmetrization. Auxiliary results and the proofs of some of the theorems are presented. Bibliography: 124 titles.
Haataja, Mikko; Gránásy, László; Löwen, Hartmut
2010-08-01
Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical density functional theory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid
Supersymmetric extensions of K field theories
Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.
2012-02-01
We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.
Families and degenerations of conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Roggenkamp, D.
2004-09-01
In this work, moduli spaces of conformal field theories are investigated. In the first part, moduli spaces corresponding to current-current deformation of conformal field theories are constructed explicitly. For WZW models, they are described in detail, and sigma model realizations of the deformed WZW models are presented. The second part is devoted to the study of boundaries of moduli spaces of conformal field theories. For this purpose a notion of convergence of families of conformal field theories is introduced, which admits certain degenerated conformal field theories to occur as limits. To such a degeneration of conformal field theories, a degeneration of metric spaces together with additional geometric structures can be associated, which give rise to a geometric interpretation. Boundaries of moduli spaces of toroidal conformal field theories, orbifolds thereof and WZW models are analyzed. Furthermore, also the limit of the discrete family of Virasoro minimal models is investigated. (orig.)
Treatise on classical elasticity theory and related problems
Teodorescu, Petre P
2013-01-01
Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University o...
Morse theory interpretation of topological quantum field theories
International Nuclear Information System (INIS)
Labastida, J.M.F.
1989-01-01
Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)
Comparison of classical and modern theories of longitudinal wave propagation in elastic rods
CSIR Research Space (South Africa)
Shatalov, M
2011-01-01
Full Text Available Conference on Computational and Applied Mechanics SACAM10 Pretoria, 10?13 January 2010 ? SACAM COMPARISON OF CLASSICAL AND MODERN THEORIES OF LONGITUDINAL WAVE PROPAGATION IN ELASTIC RODS M. Shatalov*,?,?? , I. Fedotov? 1 , HM. Tenkam? 2, J. Marais..., Pretoria, 0001 FIN-40014, South Africa 1fedotovi@tut.ac.za, 2djouosseutenkamhm@tut.ac.za ?? Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa Keywords: Elastic rod, wave propagation, classical...
Criticism of the Classical Theory of Macroeconomic Modeling
Directory of Open Access Journals (Sweden)
Konstantin K. Kumehov
2015-01-01
Full Text Available Abstract: Current approaches and methods of modeling of macroeconomic systems do not allow to generate research ideas that could be used in applications. This is largely due to the fact that the dominant economic schools and research directions are building their theories on misconceptions about the economic system as object modeling, and have no common methodological approaches in the design of macroeconomic models. All of them are focused on building a model aimed at establishing equilibrium parameters of supply and demand, production and consumption. At the same time as the underlying factors are not considered resource potential and the needs of society in material and other benefits. In addition, there is no unity in the choice of elements and mechanisms of interaction between them. Not installed, what are the criteria to determine the elements of the model: whether it is the institutions, whether the industry is whether the population, or banks, or classes, etc. From the methodological point of view, the design of the model all the most well-known authors extrapolated to the new models of the past state or past events. As a result, every time the model is ready by the time the situation changes, the last parameters underlying the model are losing relevance, so at best, the researcher may have to interpret the events and parameters that are not feasible in the future. In this paper, based on analysis of the works of famous authors, belonging to different schools and areas revealed weaknesses of their proposed macroeconomic models that do not allow you to use them to solve applied problems of economic development. A fundamentally new approaches and methods by which it is possible the construction of macroeconomic models that take into account the theoretical and applied aspects of modeling, as well as formulated the basic methodological requirements.
BRST field theory of relativistic particles
International Nuclear Information System (INIS)
Holten, J.W. van
1992-01-01
A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. The authors discuss their quantization, gauge fixing and the derivation of propagators. It is shown, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions. (author). 22 refs
Energy flow in non-equilibrium conformal field theory
Bernard, Denis; Doyon, Benjamin
2012-09-01
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.
On possibility of agreement of quantum mechanics with classical probability theory
International Nuclear Information System (INIS)
Slavnov, D.A.
2006-01-01
Paper describes a scheme to carry out a construction of the quantum mechanics where the quantum system is assumed to be a pattern of the open classical subsystems. It enables to make use both of the formal classical logic and the classical probability theory in the quantum mechanics. On the other hand, in terms of the mentioned approach one manages to ensure complete reconstruction of the quantum mechanics standard mathematical tool specifying its application limits. The problem dealing with the quantum state reduction is scrutinized [ru
An introduction to effective field theory
International Nuclear Information System (INIS)
Donoghue, John F.
1999-01-01
In these lectures I describe the main ideas of effective field theory. These are first illustrated using QED and the linear sigma model as examples. Calculational techniques using both Feynman diagrams and dispersion relations are introduced. Within QCD, chiral perturbation theory is a complete effective field theory, and I give a guide to some calculations in the literature which illustrates key ideas. (author)
String fields, higher spins and number theory
Polyakov, Dimitri
2018-01-01
The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.
International Nuclear Information System (INIS)
Astapenko, V.A.; Bureeva, L.A.; Lisitsa, V.S.
2000-01-01
Classical and quantum theories of polarization bremsstrahlung in a statistical (Thomas-Fermi) potential of complex atoms and ions are developed. The basic assumptions of the theories correspond to the approximations employed earlier in classical and quantum calculations of ordinary bremsstrahlung in a static potential. This makes it possible to study on a unified basis the contribution of both channels in the radiation taking account of their interference. The classical model makes it possible to obtain simple universal formulas for the spectral characteristics of the radiation. The theory is applied to electrons with moderate energies, which are characteristic for plasma applications, specifically, radiation from electrons on the argon-like ion KII at frequencies close to its ionization potential. The computational results show the importance of taking account of the polarization channel of the radiation for plasma with heavy ions
A post-classical theory of enamel biomineralization… and why we need one.
Simmer, James P; Richardson, Amelia S; Hu, Yuan-Yuan; Smith, Charles E; Ching-Chun Hu, Jan
2012-09-01
Enamel crystals are unique in shape, orientation and organization. They are hundreds of thousands times longer than they are wide, run parallel to each other, are oriented with respect to the ameloblast membrane at the mineralization front and are organized into rod or interrod enamel. The classical theory of amelogenesis postulates that extracellular matrix proteins shape crystallites by specifically inhibiting ion deposition on the crystal sides, orient them by binding multiple crystallites and establish higher levels of crystal organization. Elements of the classical theory are supported in principle by in vitro studies; however, the classical theory does not explain how enamel forms in vivo. In this review, we describe how amelogenesis is highly integrated with ameloblast cell activities and how the shape, orientation and organization of enamel mineral ribbons are established by a mineralization front apparatus along the secretory surface of the ameloblast cell membrane.
Gomes, Diogo A.
2016-01-06
We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.
Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana
2016-01-01
We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.
A philosophical approach to quantum field theory
Öttinger, Hans Christian
2015-01-01
This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.
Introduction to symmetry and supersymmetry in quantum field theory
International Nuclear Information System (INIS)
Lopuszanski, J.
1988-01-01
This is a set of lecture notes given by the author at the Universities of Gottingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one- semester course for graduate students in the field of mathematical physics and high energy physics. Contents: Introduction; Example of a Classical and Quantum Scalar Free Field Theory; Scene and Subject of the Drama. Axiom 1 and 2; Subject of the Drama; Principle of Relativity. Causality. Axiom 3, 4 and 5; Irreducibility of the Field Algebra and Scattering Theory. Axiom 6. Axiom O; Preliminaries about Physical Symmetries; Currents and Charges; Global Symmetries and Supersymmetries of the S - Matrix; Representations of the Super-Lie Algebra; The Case of Massless Particles; Fermionic Charges; Concluding Remarks
Classical and quantum contents of solvable game theory on Hilbert space
International Nuclear Information System (INIS)
Cheon, Taksu; Tsutsui, Izumi
2006-01-01
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation
Further Development of HS Field Theory
Abdurrahman, Abdulmajeed; Faridani, Jacqueline; Gassem, Mahmoud
2006-04-01
We present a systematic treatment of the HS Field theory of the open bosonic string and discuss its relationship to other full string field theories of the open bosonic string such as Witten's theory and the CVS theory. In the development of the HS field theory we encounter infinite dimensional matrices arising from the change of representation between the two theories, i.e., the HS field theory and the full string field theory. We give a general procedure of how to invert these gigantic matrices. The inversion of these matrices involves the computation of many infinite sums. We give the values of these sums and state their generalizations arising from considering higher order vertices (i.e., more than three strings) in string field theory. Moreover, we give a general procedure, on how to evaluate the generalized sums, that can be extended to many generic sums of similar properties. We also discuss the conformal operator connecting the HS field theory to that of the CVS string field theory.
Toward a gauge field theory of gravity.
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Algebraic construction of interacting higher spin field theories
International Nuclear Information System (INIS)
Fougere, F.
1991-10-01
We develop a general framework which we believe may provide some insights into the structure of interacting 'high spin' field theories. A finite or infinite set of classical spin fields is described by means of a field defined on an enlarged spacetime manifold. The free action and its gauge symmetries are gathered into a nilpotent differential operator on this manifold. In particular, the choice of Grassmann-valued extra coordinates leads to theories involving only a finite set of fields, the possible contents (spin multiplicities, degree of reducibility, etc.) of which are classified according to the representations of a unitary algebra. The interacting theory is characterized by a functional of the field on the enlarged manifold. We show that there is among these functionals a natural graded Lie algebra structure allowing one to rewrite the gauge invariance condition of the action in a concise form which is a nonlinear generalization of the nilpotency condition of the free theory. We obtain the general solution of this 'classical master equation' , which can be built recurrently starting form the cubic vertex, and we study its symmetries. Our formalism lends itself to a systematic introduction of additional conditions, such as locality, polynomiality, etc. We write down the general form of the solutions exhibiting a scale invariance. The case of a spin 1 field yields, as a unique solution, Yang-Mills theory. In view of quantization, we show that the solution of the classical master equation straightforwardly provides a solution of the (quantum) Batalin-Vilkoviski master equation. One may then obtain a gauge fixed action in the usual way