
Symplectic Techniques in Physics
Cambridge University Press
Published on 27. April 1984
Book
Hardback
464 pages
978-0-521-24866-2 (ISBN)
Article exhausted; check for reprint
Description
Symplectic geometry is very useful for clearly and concisely formulating problems in classical physics and also for understanding the link between classical problems and their quantum counterparts. It is thus a subject of interest to both mathematicians and physicists, though they have approached the subject from different view points. This is the first book that attempts to reconcile these approaches. The authors use the uncluttered, coordinate-free approach to symplectic geometry and classical mechanics that has been developed by mathematicians over the course of the last thirty years, but at the same time apply the apparatus to a great number of concrete problems. In the first chapter, the authors provide an elementary introduction to symplectic geometry and explain the key concepts and results in a way accessible to physicists and mathematicians. The remainder of the book is devoted to the detailed analysis and study of the ideas discussed in Chapter 1. Some of the themes emphasized in the book include the pivotal role of completely integrable systems, the importance of symmetries, analogies between classical dynamics and optics, the importance of symplectic tools in classical variational theory, symplectic features of classical field theories, and the principle of general covariance. This work can be used as a textbook for graduate courses, but the depth of coverage and the wealth of information and application means that it will be of continuing interest to, and of lasting significance for mathematicians and mathematically minded physicists.
Reviews / Votes
"This book is brilliant and fascinating and is probably one of the most important additions in recent years to the mathematical physics literature." Contemporary PhysicsMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 228 mm
Width: 152 mm
Weight
775 gr
ISBN-13
978-0-521-24866-2 (9780521248662)
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Schweitzer Classification
Other editions
New editions

Victor Guillemin | Shlomo Sternberg
Symplectic Techniques in Physics
Book
05/1990
Cambridge University Press
€81.60
Available immediately
Additional editions

Victor Guillemin | Shlomo Sternberg
Symplectic Techniques in Physics
Book
05/1990
Cambridge University Press
€81.60
Available immediately
Persons
Author
Massachusetts Institute of Technology
Harvard University, Massachusetts
Content
Preface; 1. Introduction; 2. The geometry of the moment map; 3. Motion in a Yang-Mills field and the principle of general covariance; 4. Complete integrability; 5. Contractions of symplectic homogeneous spaces; References; Index.