Geometry and quantum field theory : [notes from the 1991 Summer School on the Geometry and Topology of Manifolds and Quantum Field Theory, June 22 - July 20, 1991, in Park City, Utah

The knowledge of the interactions of photons with hadrons has considerably improved with the study of high-energy lepton-proton collisions at HERA. The results on the partonic interactions of photons are summarized in comparison with photon-nucleon, two-photon, and proton-antiproton experiments 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. Exploring topics from classical and quantum mechnanics 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 the book should provide suitable material for graduate courses. Explores topics from classical and quantum mechanics and field theory. This book covers Lie groups and symplectic geometry, examining the connection with mechanics and the application to differential equations and the work of the Gromov school. It also describes the application of supersymmetry to prove the Atiyah-Singer index theorem. Daniel S. Freed, Karen K. Uhlenbeck, Editors. Includes Bibliographical References (p. 451-453) And Indexes.