**Contemporary Mathematics**

Volume: 260;
2000;
132 pp;
Softcover

MSC: Primary 81;

Print ISBN: 978-0-8218-2115-2

Product Code: CONM/260

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

**Electronic ISBN: 978-0-8218-7850-7
Product Code: CONM/260.E**

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

# First Summer School in Analysis and Mathematical Physics: Quantization, the Segal-Bargmann Transform and Semiclassical Analysis

Share this page *Edited by *
*Salvador Pérez-Esteva; Carlos Villegas-Blas*

The first Summer School of Analysis and Mathematical Physics of the Universidad Nacional Autónoma de México (Cuernavaca) offered graduate and advanced undergraduate students courses on modern topics in the overlap between analysis and physics. This volume contains the expanded notes from the lectures by Brian Hall, Alejandro Uribe, and David Borthwick. The articles introduce readers to mathematical methods of classical and quantum mechanics and the link between these two theories: quantization and semiclassical analysis. Hall writes about holomorphic methods in analysis and mathematical physics and includes exercises. Uribe's lectures covered trace formulae, in particular asymptotic behavior and the relationship between the asymptotics and the geometric properties of the classical system. Borthwick presents an introduction to Kähler quantization, including the moment map, the orbit method, and symmetry and reduction. The exposition in the entire volume is geared to introducing graduate students with a basic knowledge of mathematics into areas of active research.

This book is published in cooperation with Sociedad Matemática Mexicana

#### Readership

Graduate students and research mathematicians interested in mathematical physics and analysis.

# Table of Contents

## First Summer School in Analysis and Mathematical Physics: Quantization, the Segal-Bargmann Transform and Semiclassical Analysis

- Contents vii8 free
- Introduction ix10 free
- Holomorphic methods in analysis and mathematical physics 114 free
- 1. Introduction 114
- 2. Basics of holomorphic function spaces 215
- 3. Examples of holomorphic function spaces 720
- 4. A special property of the Segal-Bargmann and weighted Bergman spaces 1225
- 5. Canonical commutation relations 1629
- 6. The Segal-Bargmann transform 2134
- 7. Quantum mechanics and quantization 3043
- 8. Toeplitz operators, anti-Wick ordering, and phase space probability densities 3851
- 9. The Segal-Bargmann transform for compact Lie groups 4457
- 10. To infinity and beyond 5265
- References 5871

- Trace formulae 6174
- Introduction to Kähler quantization 91104
- 1. Introduction 92105
- 2. Classical mechanics and symplectic geometry 92105
- 3. Quantization 95108
- 4. Geometric quantization 98111
- 5. Complex geometry and Kähler manifolds 100113
- 6. Kähler quantization 102115
- 7. Euclidean Cn 103116
- 8. Complex projective space 106119
- 9. Orbits and representation theory 108121
- 10. Symmetry and reduction 112125
- 11. Quantizing principal bundle 115128
- 12. Coherent states 117130
- 13. Semiclassical analysis 120133
- 14. Spectral asymptotics 124137
- 15. Riemann surfaces 125138
- 16. Almost-Kähler quantization 129142
- References 131144