Geometry and Quantum Field Theory
About this Title
Daniel S. Freed, University of Texas at Austin and Karen K. Uhlenbeck, University of Texas at Austin, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 1995; Volume 1
ISBNs: 978-0-8218-0400-1 (print); 978-1-4704-3900-2 (online)
MathSciNet review: MR1338390
MSC: Primary 00B25; Secondary 58-06, 81-06
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.
Research mathematicians, graduate students in mathematics, and physicists.
Table of Contents
- An introduction to Lie groups and symplectic geometry
- Introduction to quantum field theory for mathematicians
- Lectures on quantum mechanics and the index theorem
- Lectures on axiomatic topological quantum field theory