**Contemporary Mathematics**

Volume: 179;
1994;
285 pp;
Softcover

MSC: Primary 58; 81;
Secondary 22; 46

Print ISBN: 978-0-8218-0302-8

Product Code: CONM/179

List Price: $67.00

Individual Member Price: $53.60

**Electronic ISBN: 978-0-8218-7770-8
Product Code: CONM/179.E**

List Price: $67.00

Individual Member Price: $53.60

# Symplectic Geometry and Quantization

Share this page *Edited by *
*Yoshiaki Maeda; Hideki Omori; Alan Weinstein*

This volume contains the refereed proceedings of two symposia on symplectic geometry and quantization problems which were held in Japan in July 1993. The purpose of the symposia was to discuss recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, noncommutative differential geometry, equivariant cohomology, deformation quantization, topological quantum field theory, and knot invariants. The book provides insight into how these different topics relate to one another and offers intriguing new problems. Providing a look at the frontier of research in symplectic geometry and quantization, this book is suitable as a source book for a seminar in symplectic geometry.

#### Readership

Graduate students and researchers

# Table of Contents

## Symplectic Geometry and Quantization

- Contents vii8 free
- Preface ix10 free
- Some remarks on the classification of Poisson Lie groups 112 free
- Lie groups and algebras in infinite dimension: A new approach 1728
- Equivariant cohomology and statidnary phase 4556
- The Bargmann representation, generalized Dirac operators, and the index of pseudodifferential operators on Rn 6374
- Quantization by means of two-dimensional surfaces (membranes): Geometrical formulas for wave-functions 8394
- Geometric star products 115126
- Vassiliev invariants and de Rham complex on the space of knots 123134
- Geometry of loop groups and Wess-Zumino-Witten models 139150
- The noncommutative algebra of the quantum group SUq(2) as a quantized Poisson manifold 161172
- Symplectic and Poisson structures on some loop groups 173184
- The Euler and Godbillon-Vey forms and symplectic structures on Dif f∞+(S1)/SO(2) 193204
- A Tau-function for the finite Toda molecule, and information spaces 205216
- Deformation quantizations of Poisson algebras 213224
- An analogue of Edmonds' theorem for loop spaces 241252
- Traces and triangles in symmetric symplectic space 261272
- Geometric quantization of Poisson groups—Diagonal and soft deformations 271282