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Nonlinear Poisson Brackets: Geometry and Quantization
 
Nonlinear Poisson Brackets
Softcover ISBN:  978-0-8218-8796-7
Product Code:  MMONO/119.S
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-1619-5
Product Code:  MMONO/119.S.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-8796-7
eBook: ISBN:  978-1-4704-1619-5
Product Code:  MMONO/119.S.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Nonlinear Poisson Brackets
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Nonlinear Poisson Brackets: Geometry and Quantization
Softcover ISBN:  978-0-8218-8796-7
Product Code:  MMONO/119.S
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-1619-5
Product Code:  MMONO/119.S.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-8796-7
eBook ISBN:  978-1-4704-1619-5
Product Code:  MMONO/119.S.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1191993; 366 pp
    MSC: Primary 58; 81; 03; Secondary 16; 05;

    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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. Poisson manifolds
    • Chapter 2. Analog of the group operation for nonlinear Poisson brackets
    • Chapter 3. Poisson brackets in $R^{2n}$ and semi-classical approximation
    • Chapter 4. Asymptotic quantization
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1191993; 366 pp
MSC: Primary 58; 81; 03; Secondary 16; 05;

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.

  • Chapters
  • Introduction
  • Chapter 1. Poisson manifolds
  • Chapter 2. Analog of the group operation for nonlinear Poisson brackets
  • Chapter 3. Poisson brackets in $R^{2n}$ and semi-classical approximation
  • Chapter 4. Asymptotic quantization
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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