Nonlinear Poisson Brackets. Geometry and Quantization (Translations of Mathematical Monographs) - Hardcover

M. V. Karasev And V. P. Maslov

Hardcover

ISBN 10: 0821845969 ISBN 13: 9780821845967

Publisher: American Mathematical Society, 1993

Synopsis

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• Language: English
• ISBN 10: 0821845969
• ISBN 13: 9780821845967
• Binding: Hardcover
• Number of pages: 366