Symplectic Techniques in Physics - Hardcover

Guillemin, Victor; Sternberg, Shlomo

Hardcover

ISBN 10: 0521248663 ISBN 13: 9780521248662

Publisher: Cambridge University Press, 1984

Synopsis

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.

About this title

Review

"This book is brilliant and fascinating and is probably one of the most important additions in recent years to the mathematical physics literature." Contemporary Physics

Edition details

• Publisher: Cambridge University Press
• Publication date: 1984
• ISBN 10: 0521248663
• ISBN 13: 9780521248662
• Binding: Hardcover
• Language: English
• Number of pages: 464