Mathematical Aspects Of Classical Field Theory

Author : Mark J. Gotay,Jerrold E. Marsden,Vincent Moncrief
Publisher : American Mathematical Soc.
Page : 644 pages
File Size : 48,5 Mb
Release : 1992
Category : Science
ISBN : 9780821851449

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Mathematical Aspects of Classical Field Theory by Mark J. Gotay,Jerrold E. Marsden,Vincent Moncrief Pdf

Classical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject.

Author : Damien Calaque,Thomas Strobl
Publisher : Springer
Page : 572 pages
File Size : 51,7 Mb
Release : 2015-01-06
Category : Science
ISBN : 9783319099491

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Mathematical Aspects of Quantum Field Theories by Damien Calaque,Thomas Strobl Pdf

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 homology and factorization algebras.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 644 pages
File Size : 43,9 Mb
Release : 1992
Category : Field theory (Physics)
ISBN : 0821854674

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Mathematical aspects of classical field theory by Anonim Pdf

Author : Edson de Faria,Welington de Melo
Publisher : Cambridge University Press
Page : 128 pages
File Size : 45,5 Mb
Release : 2010-08-12
Category : Science
ISBN : 9781139489805

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Mathematical Aspects of Quantum Field Theory by Edson de Faria,Welington de Melo Pdf

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.

Author : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 48,6 Mb
Release : 2007-07-05
Category : Mathematics
ISBN : 9783540489269

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Mathematical Aspects of Classical and Celestial Mechanics by Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt Pdf

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Author : Andrej Tyurin
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 54,7 Mb
Release : 2003
Category : Functions, Theta
ISBN : 9780821832400

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Quantization, Classical and Quantum Field Theory and Theta Functions by Andrej Tyurin Pdf

This book is written by a well-known expert in classical algebraic geometry. Tyurin's research was specifically in explicit computations to vector bundles on algebraic varieties. This is the only available monograph written from his unique viewpoint. Ordinary (abelian) theta functions describe properties of moduli spaces of one-dimensional vector bundles on algebraic curves. Non-abelian theta functions, which are the main topic of this book, play a similar role in the study of higher-dimensional vector bundles. The book presents various aspects of the theory of non-abelian theta functions and the moduli spaces of vector bundles, including their applications to problems of quantization and to classical and quantum conformal field theories. The book is an important source of information for specialists in algebraic geometry and its applications to mathematical aspects of quantum field theory.

Author : Ernst Binz,Jedrzej Sniatycki
Publisher : Courier Corporation
Page : 474 pages
File Size : 43,7 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486150444

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Geometry of Classical Fields by Ernst Binz,Jedrzej Sniatycki Pdf

A canonical quantization approach to classical field theory, this text is suitable for mathematicians interested in theoretical physics as well as to theoretical physicists who use differential geometric methods in their modelling. Introduces differential geometry, the theory of Lie groups, and progresses to discuss the systematic development of a covariant Hamiltonian formulation of field theory. 1988 edition.

Author : Martin Schottenloher
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 54,8 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540706908

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A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher Pdf

Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.

Author : G. Giachetta
Publisher : World Scientific
Page : 393 pages
File Size : 43,8 Mb
Release : 2009
Category : Science
ISBN : 9789812838964

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Advanced Classical Field Theory by G. Giachetta Pdf

Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.

Author : Walter Thirring
Publisher : Springer
Page : 270 pages
File Size : 45,6 Mb
Release : 2014-07-08
Category : Science
ISBN : 9781441987624

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A Course in Mathematical Physics 2 by Walter Thirring Pdf

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 Kaluza-Klein theories and in cosmology, but I felt bound to my promise not to burden the students with theoretical speculations for which there is no experimental evidence. I am indebted to many people for suggestions concerning this volume. In particular, P. Aichelburg, H. Rumpf and H. Urbantke have contributed generously to corrections and improvements. Finally, I would like to thank Dr. 1. Dahl-Jensen for redoing some of the figures on the computer.

Author : Frédéric Paugam
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 40,7 Mb
Release : 2014-02-20
Category : Science
ISBN : 9783319045641

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Towards the Mathematics of Quantum Field Theory by Frédéric Paugam Pdf

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.

Author : Paul Sally
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 52,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851869

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Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups by Paul Sally Pdf

This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.

Author : V.I. Arnold,Victor V. Kozlov,A.I. Neishtadt
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 53,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642612374

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Mathematical Aspects of Classical and Celestial Mechanics by V.I. Arnold,Victor V. Kozlov,A.I. Neishtadt Pdf

From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989

Author : Walter Thirring
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 48,8 Mb
Release : 2003-10-17
Category : Science
ISBN : 0387406158

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Classical Mathematical Physics by Walter Thirring Pdf

This volume combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and pertubation theory. Problems discussed in considerable detail include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differenial geometry throughout, treating both Maxwell's and Einstein's equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds; it concludes by applying these results to the life and death of stars.

Author : L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili
Publisher : World Scientific
Page : 516 pages
File Size : 54,9 Mb
Release : 2000
Category : Science
ISBN : 9789810220136

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Connections in Classical and Quantum Field Theory by L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili Pdf

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.