2022-05-28T16:22:43Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/452752018-01-24T16:44:42Zhdl_2115_45007hdl_2115_116Path Integral Representation of the Index of Kahler-Dirac Operators on an Infinite Dimensional ManifoldArai, A.81-xx QUANTUM THEORY410Operators of Kahler-Dirac type are defined in an abstract infinite dimensional Boson-Fermion Fock space and a path integral representation of their index is established. As preliminaries to this end, some trace formulas associated with "Gibbs states" are derived in both an abstract Boson and Fermion Fock space. This is done by introducing Euclidean Bose and Fermi fields at "finite temperature" in each case. In connection with supersymmetric. quantum field theories, the result gives a path integral formula of the so-called "Witten index" in a model with cutoffs.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/45275info:doi/10.14943/48865https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/45275/5/pre3.pdfHokkaido University Preprint Series in Mathematics31681987-06engpublisher