Nonlinear Poisson Brackets
：Geometry and Quantization
( Translations of Mathematical Monographs )
Publication subTitle ：Geometry and Quantization
Publication series ： Translations of Mathematical Monographs
Author： M. V. Karasev;V. P. Maslov
Publisher： American Mathematical Society
Publication year： 2012
E-ISBN: 9781470416195
P-ISBN(Paperback): 9780821887967
Subject： O189.3 analytical topology
Keyword： 数学
Language： ENG
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Nonlinear Poisson Brackets
Description
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.
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