Geometry and quantum field theory
著者
書誌事項
Geometry and quantum field theory
（IAS/Park City mathematics series / [Dan Freed, series editor], v. 1）
American Mathematical Society : Institute for Advanced Study, c1995
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独立行政法人国立高等専門学校機構 香川高等専門学校 高松キャンパス 図書館
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注記
"Lecture notes from the Graduate Summer School Program on the Geometry and Topology of Manifolds and Quantum Field Theory, held June 22-July 20, 1991, in Park City, Utah" -- T.p. verso
Bibliography: p. 451-453
Includes indexes
内容説明・目次
内容説明
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.
目次
An introduction to Lie groups and symplectic geometry by R. L. Bryant Introduction to quantum field theory for mathematicians by J. M. Rabin Lectures on quantum mechanics and the index theorem by O. Alvarez Lectures on axiomatic topological quantum field theory by F. S. Quinn.
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