Nonlinear Poisson Brackets: Geometry and Quantization
M. V. Karasev and V. P. Maslov
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.
Readership: Graduate students and researchers
Readership: Graduate students and researchers
Категории:
Год:
1993
Издательство:
American Mathematical Society
Язык:
english
ISBN 10:
0821887963
ISBN 13:
9780821887967
Серия:
Translations of Mathematical Monographs, Vol. 119
Файл:
PDF, 5.02 MB
IPFS:
,
english, 1993