**CRM Monograph Series**

Volume: 21;
2003;
136 pp;
Hardcover

MSC: Primary 53;
Secondary 14; 57; 81

Print ISBN: 978-0-8218-3240-0

Product Code: CRMM/21

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-4704-3866-1
Product Code: CRMM/21.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

#### Supplemental Materials

# Quantization, Classical and Quantum Field Theory and Theta Functions

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*Andrei Tyurin*

A co-publication of the AMS and Centre de Recherches Mathématiques

This book is written by a well-known expert in classical algebraic
geometry. Tyurin's research was specifically in explicit computations to vector
bundles on algebraic varieties. This is the only available monograph written
from his unique viewpoint.

Ordinary (abelian) theta functions describe properties of moduli spaces of
one-dimensional vector bundles on algebraic curves. Non-abelian theta
functions, which are the main topic of this book, play a similar role in the
study of higher-dimensional vector bundles. The book presents various aspects
of the theory of non-abelian theta functions and the moduli spaces of vector
bundles, including their applications to problems of quantization and to
classical and quantum conformal field theories.

The book is an important source of information for specialists in algebraic
geometry and its applications to mathematical aspects of quantum field
theory.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and its applications to mathematical physics.

#### Reviews & Endorsements

The book opens a beautiful and grandiose view to a fascinating part of geometry, notably symplectic and algebraic geometry, and, as usual in Andrei Tyurin's work, it has a very geometric flavor. ...The ideal reader should preferably dispose of some basic knowledge of classical algebraic geometry or theory of Riemann surfaces and of symplectic geometry, then he will benefit quite a lot from reading this book.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Quantization, Classical and Quantum Field Theory and Theta Functions

- Cover Cover11
- Title page iii4
- Dedication v6
- Photo vi7
- Foreword vii8
- Introduction ix10
- Contents xi12
- Quantization procedure 114
- Algebraic curves = Riemann surfaces 1730
- Non-abelian theta functions 2942
- Symplectic geometry of moduli spaces of vector bundles 5366
- Two versions of CQFT 6376
- Three-valent graphs 7184
- Analytical aspects of the theory of non-abelian theta functions 101114
- BPU-map 107120
- The main weapon 117130
- Bibliography 133146
- Back Cover Back Cover1150