Nonlinear Poisson brackets : geometry and quantization
著者
書誌事項
Nonlinear Poisson brackets : geometry and quantization
（Translations of mathematical monographs, v. 119）
American Mathematical Society, c1993
- タイトル別名
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Нелинейные скобки Пуассона : геометрия и квантование
Nelineĭnye skobki Puassona : geometrii︠a︡ i kvantovanie
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注記
Includes bibliographical references (p. 353-366)
内容説明・目次
内容説明
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.
目次
Poisson manifolds Analog of the group operation for nonlinear Poisson brackets Poisson brackets in $\mathbb R^2n$ and semiclassical approximation Asymptotic quantization Appendix I: Formulas of noncommutative analysis II: Calculus of symbols and commutation relations.
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