Symplectic Techniques in Physics

ISBN-13: 9780521389907 / Angielski / Miękka / 1990 / 484 str.

Victor W. Guillemin; Shlomo Sternberg

Opis

Symplectic geometry is very useful for formulating clearly and concisely 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 viewpoints. 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 past thirty years, but at the same time apply the apparatus to a great number of concrete problems. 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.

Recenzje

"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

Spis treści

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.