Mathematical Aspects Of Classical Field Theory PDF Download
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Author | : Mark J. Gotay |
Publisher | : American Mathematical Soc. |
Total Pages | : 658 |
Release | : 1992 |
Genre | : Science |
ISBN | : 0821851446 |
Download Mathematical Aspects of Classical Field Theory Book in PDF, ePub and Kindle
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.
Author | : Damien Calaque |
Publisher | : Springer |
Total Pages | : 572 |
Release | : 2015-01-06 |
Genre | : Science |
ISBN | : 3319099493 |
Download Mathematical Aspects of Quantum Field Theories Book in PDF, ePub and Kindle
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 | : |
Publisher | : American Mathematical Soc. |
Total Pages | : 644 |
Release | : 1992 |
Genre | : Field theory (Physics) |
ISBN | : 9780821854679 |
Download Mathematical aspects of classical field theory Book in PDF, ePub and Kindle
Author | : Edson de Faria |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2010-08-12 |
Genre | : Science |
ISBN | : 1139489801 |
Download Mathematical Aspects of Quantum Field Theory Book in PDF, ePub and Kindle
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 | : Mark J. Gotay |
Publisher | : |
Total Pages | : 644 |
Release | : 1992 |
Genre | : |
ISBN | : |
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Author | : G. Giachetta |
Publisher | : World Scientific |
Total Pages | : 393 |
Release | : 2009 |
Genre | : Science |
ISBN | : 9812838961 |
Download Advanced Classical Field Theory Book in PDF, ePub and Kindle
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 | : Vladimir I. Arnold |
Publisher | : Springer Science & Business Media |
Total Pages | : 505 |
Release | : 2007-07-05 |
Genre | : Mathematics |
ISBN | : 3540489266 |
Download Mathematical Aspects of Classical and Celestial Mechanics Book in PDF, ePub and Kindle
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 | : V.I. Arnol'd |
Publisher | : Springer Science & Business Media |
Total Pages | : 530 |
Release | : 2013-04-09 |
Genre | : Mathematics |
ISBN | : 1475720637 |
Download Mathematical Methods of Classical Mechanics Book in PDF, ePub and Kindle
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.
Author | : Pierre Deligne |
Publisher | : American Mathematical Society |
Total Pages | : 801 |
Release | : 1999-10-25 |
Genre | : Mathematics |
ISBN | : 0821820133 |
Download Quantum Fields and Strings: A Course for Mathematicians Book in PDF, ePub and Kindle
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.
Author | : Walter Thirring |
Publisher | : Springer |
Total Pages | : 270 |
Release | : 2014-07-08 |
Genre | : Science |
ISBN | : 1441987622 |
Download A Course in Mathematical Physics 2 Book in PDF, ePub and Kindle
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.