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Path Integral Representation of the Index of Kahler-Dirac Operators on an Infinite Dimensional Manifold
| Title: | Path Integral Representation of the Index of Kahler-Dirac Operators on an Infinite Dimensional Manifold |
| Authors: | Arai, A. Browse this author →KAKEN DB |
| Keywords: | 81-xx QUANTUM THEORY |
| Issue Date: | Jun-1987 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 3 |
| Start Page: | 1 |
| End Page: | 68 |
| Abstract: | Operators 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. |
| Description: | This work was supported by the Grant-In-Aid, No.62740072 and No.6246000l for science research from the Ministry of Education ( Japan ). |
| Type: | bulletin (article) |
| URI: | http://eprints3.math.sci.hokudai.ac.jp/420/ | | http://hdl.handle.net/2115/45275 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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