Topological Quantum Theories and Representation Theory
We discuss the relationship between path integrals, geometric quantization and representation theory for a simple quantum theory whose Hilbert space is a group representation. The path integrals involved have interesting cohomological significance and can be evaluated in terms of fixed point formulas to give the Kirillov and Weyl character formulas. The relation to recent work of Witten on Chern-Simons gauge theory is also discussed.
KeywordsLine Bundle Dirac Operator Loop Space Holomorphic Section Geometric Quantization
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