Symplectic Techniques in Physics
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Symplectic Techniques in Physics by Victor Guillemin
Book DescriptionSymplectic 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.
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Book DetailsISBN: 9780521389907
(228mm x 152mm x 27mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 25-May-1990
Country of Publication: United Kingdom
Books By Author Victor Guillemin
Symplectic Fibrations and Multiplicity Diagrams, Paperback (June 2009)
Applications of the techniques of symplectic geometry to describe 'symmetry breaking' in quantum physics.
Story of Quantum Mechanics, Paperback (June 2003)View all books by Victor Guillemin
Written by a renowned MIT mathematician, this introduction to the evolution of quantum physics also explores philosophical implications, including issues of causality, determinism, and free will. 48 illustrations. 1968 edition.
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