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Author: Mark J. Gotay Publisher: American Mathematical Soc. ISBN: 0821851446 Category : Science Languages : en Pages : 658
Book Description
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: Mark J. Gotay Publisher: American Mathematical Soc. ISBN: 0821851446 Category : Science Languages : en Pages : 658
Book Description
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: A. P. Balachandran Publisher: World Scientific ISBN: 9789810203290 Category : Mathematics Languages : en Pages : 386
Book Description
This book is an introduction to the role of topology in the quantization of classical systems. It is also an introduction to topological solitons with special emphasis on Skyrmions. As regards the first aspect, several issues of current interest are dealt with at a reasonably elementary level. Examples are principal fibre bundles and their role in quantum physics, the possibility of spinorial quantum states in a Lagrangian theory based on tensorial variables, and multiply connected configuration spaces and associated quantum phenomena like the QCD q angle and exotic statistics. The ideas are also illustrated by simple examples such as the spinning particle, the charge-monopole system and strings in 3+1 dimensions. The application of these ideas to quantum gravity is another subject treated at an introductory level. An attempt has been made in this book to introduce the reader to the significance of topology for many distinct physical systems such as spinning particles, the charge- monopole system, strings, Skyrmions, QCD and gravity. The book is an outgrowth of lectures given by the authors at various institutions and conferences.
Author: Marc Henneaux Publisher: Princeton University Press ISBN: 9780691037691 Category : Mathematics Languages : en Pages : 556
Book Description
This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.
Author: Massimo Cerdonio Publisher: #N/A ISBN: 9814699780 Category : Languages : en Pages : 650
Book Description
This conference reviewed the current status of General Relativity and Classical Theories of Gravitation, Relativistic Astrophysics and Cosmology, Experimental and Observational Gravitation, Supergravity and Quantum Gravity.
Author: S. de Filippo Publisher: Elsevier ISBN: 0444598715 Category : Science Languages : en Pages : 259
Book Description
Experts in general relativity, particle physics and mathematical physics discuss aspects of their recent research. The main emphasis is on the geometrical and algebraic methods used in solving a wide range of problems.
Author: A. Bassetto Publisher: World Scientific ISBN: 9789810205782 Category : Science Languages : en Pages : 254
Book Description
This volume deals with canonical quantization, Feynman rules and renormalization of Yang-Mills theories in algebraic non-covariant gauges (typically axial and light-cone gauges). The material is self-contained and presented in a basic manner according to a personal style representative of a long lasting activity in the field. Emphasis is always placed on the underlying basic concepts of Quantum Field Theory, even when particular examples are treated, details and the related difficulties are thoroughly discussed. The value of the book goes beyond the specificity of its subject.
Author: Jogesh C Pati Publisher: World Scientific ISBN: 9813201371 Category : Science Languages : en Pages : 666
Book Description
The ICTP has been holding a Summer Workshop in High Energy Physics and Cosmology since 1981. The primary goal of these workshops is to bring together active physicists from around the world, and to provide a platform where the frontier developments in the field are presented by leading workers. The atmosphere for the workshop was active and stimulating and each area was represented by leading physicists in the field.
Author: Sydney Coleman Publisher: World Scientific ISBN: 9814602590 Category : Languages : en Pages : 367
Book Description
The subject of Quantum Cosmology is concerned with providing a quantum mechanical description of the universe as a whole and, within that description, to constructing a theory of the universe's initial condition whose predictions can be compared with observation. The recent progress in this area has profound implications for physics at all scales. The lectures at this School describe these theories and their implications. They cover basic quantum mechanics of cosmology, proposals for theories of initial conditions, and their application to the prediction of the large scale features of our universe. A special emphasis of the School is the implication of topological fluctuations of spacetime (wormholes, baby universes) for the observed coupling constants of the low energy interactions of elementary particles and as a potential explanation for the vanishing of the cosmological constant.
Author: Filippo Colomo Publisher: World Scientific ISBN: 9814552275 Category : Languages : en Pages : 462
Book Description
This second workshop on constraint theory aims at reviewing the developments that have taken place in the theory of singular Lagrangians and Dirac-Bergmann Hamiltonian constraints as well as their quantization. Since this theory lies behind all special and general relativistic systems, the topics covered here naturally range from mathematical physics to relativistic system particles, strings and fields and further to general relativity. The variety of topics discussed makes this an important, interesting and informative book.
Author: Mark J. Gotay
Author: Mark J. Gotay
Author: A. P. Balachandran
Author: Marc Henneaux
Author: Massimo Cerdonio
Author: S. de Filippo
Author: A. Bassetto
Author: Jogesh C Pati
Author: Sydney Coleman
Author: Filippo Colomo
Author: M. Asorey