Softcover ISBN:  9780821816790 
Product Code:  CBMS/29 
List Price:  $24.00 
Individual Price:  $19.20 
eBook ISBN:  9781470423896 
Product Code:  CBMS/29.E 
List Price:  $21.00 
Individual Price:  $16.80 
Softcover ISBN:  9780821816790 
eBook: ISBN:  9781470423896 
Product Code:  CBMS/29.B 
List Price:  $45.00 $34.50 
Softcover ISBN:  9780821816790 
Product Code:  CBMS/29 
List Price:  $24.00 
Individual Price:  $19.20 
eBook ISBN:  9781470423896 
Product Code:  CBMS/29.E 
List Price:  $21.00 
Individual Price:  $16.80 
Softcover ISBN:  9780821816790 
eBook ISBN:  9781470423896 
Product Code:  CBMS/29.B 
List Price:  $45.00 $34.50 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 29; 1977; 48 ppMSC: Primary 58; Secondary 47; 53; 70
The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.
Readership 
Table of Contents

Chapters

Introduction

Symplectic manifolds and lagrangian submanifolds, examples

Lagrangian splittings, real and complex polarizations, Kähler manifolds

Reduction, the calculus of canonical relations, intermediate polarizations

Hamiltonian systems and group actions on symplectic manifolds

Normal forms

Lagrangian submanifolds and families of functions

Intersection Theory of Lagrangian submanifolds

Quantization on cotangent bundles

Quantization and polarizations

Quantizing Lagrangian submanifolds and subspaces, construction of the Maslov bundle


Reviews

This volume of lecture notes is devoted to some problems in differential topology arising from the study of Hamiltonian systems and geometrical quantization ... After the necessary definitions are given, some topological facts and problems concerning symplectic and Lagrangian manifolds are presented and their origin in abstract Hamiltonian mechanics is outlined. The author treats the classification problem for symplectic manifolds and discusses the relevant theorems of Darboux and Moser, and comments on the embedding problem and intersection theory for Lagrangian submanifolds. The last three chapters are devoted to geometric quantization in connection with representation theory of Lie groups, the quasiclassical approximation in quantum mechanics, and the theory of Fourier integral operators. The author states several open problems and supplies a detailed bibliography.
Mathematical Reviews


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The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.

Chapters

Introduction

Symplectic manifolds and lagrangian submanifolds, examples

Lagrangian splittings, real and complex polarizations, Kähler manifolds

Reduction, the calculus of canonical relations, intermediate polarizations

Hamiltonian systems and group actions on symplectic manifolds

Normal forms

Lagrangian submanifolds and families of functions

Intersection Theory of Lagrangian submanifolds

Quantization on cotangent bundles

Quantization and polarizations

Quantizing Lagrangian submanifolds and subspaces, construction of the Maslov bundle

This volume of lecture notes is devoted to some problems in differential topology arising from the study of Hamiltonian systems and geometrical quantization ... After the necessary definitions are given, some topological facts and problems concerning symplectic and Lagrangian manifolds are presented and their origin in abstract Hamiltonian mechanics is outlined. The author treats the classification problem for symplectic manifolds and discusses the relevant theorems of Darboux and Moser, and comments on the embedding problem and intersection theory for Lagrangian submanifolds. The last three chapters are devoted to geometric quantization in connection with representation theory of Lie groups, the quasiclassical approximation in quantum mechanics, and the theory of Fourier integral operators. The author states several open problems and supplies a detailed bibliography.
Mathematical Reviews