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Quantization, Classical and Quantum Field Theory and Theta Functions

Andrei Tyurin Steklov Institute of Mathematical Sciences, Moscow, Russia
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Hardcover ISBN: 978-0-8218-3240-0
Product Code: CRMM/21
List Price: $53.00 MAA Member Price:$47.70
AMS Member Price: $42.40 Electronic ISBN: 978-1-4704-3866-1 Product Code: CRMM/21.E List Price:$50.00
MAA Member Price: $45.00 AMS Member Price:$40.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $79.50 MAA Member Price:$71.55
AMS Member Price: $63.60 Click above image for expanded view Quantization, Classical and Quantum Field Theory and Theta Functions Andrei Tyurin Steklov Institute of Mathematical Sciences, Moscow, Russia A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats:  Hardcover ISBN: 978-0-8218-3240-0 Product Code: CRMM/21  List Price:$53.00 MAA Member Price: $47.70 AMS Member Price:$42.40
 Electronic ISBN: 978-1-4704-3866-1 Product Code: CRMM/21.E
 List Price: $50.00 MAA Member Price:$45.00 AMS Member Price: $40.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$79.50 MAA Member Price: $71.55 AMS Member Price:$63.60
• Book Details

CRM Monograph Series
Volume: 212003; 136 pp
MSC: Primary 53; Secondary 14; 57; 81;

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.

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

• Chapters
• Quantization procedure
• Algebraic curves = Riemann surfaces
• Non-abelian theta functions
• Symplectic geometry of moduli spaces of vector bundles
• Two versions of CQFT
• Three-valent graphs
• Analytical aspects of the theory of non-abelian theta functions
• BPU-map
• The main weapon

• Reviews

• 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
• Request Review Copy
Volume: 212003; 136 pp
MSC: Primary 53; Secondary 14; 57; 81;

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.

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

• Chapters
• Quantization procedure
• Algebraic curves = Riemann surfaces
• Non-abelian theta functions
• Symplectic geometry of moduli spaces of vector bundles
• Two versions of CQFT
• Three-valent graphs
• Analytical aspects of the theory of non-abelian theta functions
• BPU-map
• The main weapon
• 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
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