Volume: 1; 1995; 459 pp; Softcover
MSC: Primary 58; 81; 70; 53; Secondary 16; 18; 22; 34; 35; 49
Print ISBN: 978-0-8218-0400-1
Product Code: PCMS/1
List Price: $64.00
AMS Member Price: $51.20
MAA Member Price: $57.60
Electronic ISBN: 978-1-4704-3900-2
Product Code: PCMS/1.E
List Price: $60.00
AMS Member Price: $48.00
MAA Member Price: $54.00
Geometry and Quantum Field Theory
Share this pageEdited by Daniel S. Freed; Karen K. Uhlenbeck
A co-publication of the AMS and IAS/Park City Mathematics Institute
Exploring topics from classical and quantum mechanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
Readership
Research mathematicians, graduate students in mathematics, and physicists.
Table of Contents
Geometry and Quantum Field Theory
- Cover Cover11
- Title page i2
- Preface iii4
- Contents v6
- Introduction 112
- An introduction to Lie groups and symplectic geometry 516
- Introduction to quantum field theory for mathematicians 183194
- Lectures on quantum mechanics and the index theorem 271282
- Lectures on axiomatic topological quantum field theory 323334
- Index of Notations 455466
- Index of Terminology 457468
- Back Cover Back Cover1471