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Mathematical Aspects Of Classical Field Theory
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Book Synopsis Mathematical Aspects of Classical Field Theory by : Mark J. Gotay
Download or read book Mathematical Aspects of Classical Field Theory written by Mark J. Gotay and published by American Mathematical Soc.. This book was released on 1992 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The topics fall into four major categories: global analysis and relativity (cosmic censorship, initial value problem, quantum gravity), geometric methods (symplectic and Poisson structures, momentum mappings, Dirac constraint theory), BRST theory, and the calculus of variations (the variational bicomplex, higher order theories). Also included are related topics with a ``classical basis'', such as geometric quantization, integrable systems, symmetries, deformation theory, and geometric mechanics.
Book Synopsis Mathematical Aspects of Quantum Field Theories by : Damien Calaque
Download or read book Mathematical Aspects of Quantum Field Theories written by Damien Calaque and published by Springer. This book was released on 2015-01-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical aspects of classical field theory by :
Download or read book Mathematical aspects of classical field theory written by and published by American Mathematical Soc.. This book was released on 1992 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Aspects of Quantum Field Theory by : Edson de Faria
Download or read book Mathematical Aspects of Quantum Field Theory written by Edson de Faria and published by Cambridge University Press. This book was released on 2010-08-12 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Aspects of Classical Field Theory by : Mark J. Gotay
Download or read book Mathematical Aspects of Classical Field Theory written by Mark J. Gotay and published by . This book was released on 1992 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Methods of Classical Mechanics by : V.I. Arnol'd
Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Book Synopsis Advanced Classical Field Theory by : G. Giachetta
Download or read book Advanced Classical Field Theory written by G. Giachetta and published by World Scientific. This book was released on 2009 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Aspects of Classical and Celestial Mechanics by : Vladimir I. Arnold
Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Course in Mathematical Physics 2 by : Walter Thirring
Download or read book A Course in Mathematical Physics 2 written by Walter Thirring and published by Springer. This book was released on 2014-07-08 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical Field Theory by : Horaƫiu Năstase
Download or read book Classical Field Theory written by Horaƫiu Năstase and published by Cambridge University Press. This book was released on 2019-03-14 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical field theory predicts how physical fields interact with matter, and is a logical precursor to quantum field theory. This introduction focuses purely on modern classical field theory, helping graduates and researchers build an understanding of classical field theory methods before embarking on future studies in quantum field theory. It describes various classical methods for fields with negligible quantum effects, for instance electromagnetism and gravitational fields. It focuses on solutions that take advantage of classical field theory methods as opposed to applications or geometric properties. Other fields covered includes fermionic fields, scalar fields and Chern–Simons fields. Methods such as symmetries, global and local methods, Noether theorem and energy momentum tensor are also discussed, as well as important solutions of the classical equations, in particular soliton solutions.
Book Synopsis Quantum Fields and Strings: A Course for Mathematicians by : Pierre Deligne
Download or read book Quantum Fields and Strings: A Course for Mathematicians written by Pierre Deligne and published by American Mathematical Society. This book was released on 1999-10-25 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.
Book Synopsis Quantization, Classical and Quantum Field Theory and Theta Functions by : Andrej Tyurin
Download or read book Quantization, Classical and Quantum Field Theory and Theta Functions written by Andrej Tyurin and published by American Mathematical Soc.. This book was released on 2003 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Mathematical Introduction to Conformal Field Theory by : Martin Schottenloher
Download or read book A Mathematical Introduction to Conformal Field Theory written by Martin Schottenloher and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Aspects of Classical and Celestial Mechanics by : V.I. Arnold
Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications by : Jurg Frohlich
Download or read book Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications written by Jurg Frohlich and published by World Scientific. This book was released on 1992-04-29 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.
Book Synopsis Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups by : Paul J. Sally (Jr.)
Download or read book Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups written by Paul J. Sally (Jr.) and published by American Mathematical Soc.. This book was released on 1994 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Special Relativity and Classical Field Theory by : Leonard Susskind
Download or read book Special Relativity and Classical Field Theory written by Leonard Susskind and published by Basic Books. This book was released on 2017-09-26 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume in the bestselling physics series cracks open Einstein's special relativity and field theory 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.
