The fermionic integral on loop space and the Pfaffian line bundle
- As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component " of a differential form on it. In this paper, we show that a formula from finite dimensions generalizes to assign a sensible "top degree component " to certain composite forms, obtained by wedging with the exponential (in the exterior algebra) of the canonical presymplectic 2-form on the loop space. This construction is a crucial ingredient for the definition of the supersymmetric path integral on the loop space.
| Author details: | Florian HanischGND, Matthias LudewigORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1063/5.0060355 |
| ISSN: | 0022-2488 |
| ISSN: | 1089-7658 |
| ISSN: | 1527-2427 |
| Title of parent work (English): | Journal of mathematical physics |
| Publisher: | American Inst. of Physics |
| Place of publishing: | College Park, Md. |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/12/01 |
| Publication year: | 2022 |
| Release date: | 2024/08/09 |
| Volume: | 63 |
| Issue: | 12 |
| Article number: | 123502 |
| Number of pages: | 26 |
| Funding institution: | Max-Planck Institute for Gravitational Physics in Potsdam; (Albert-Einstein-Institute); Max-Planck-Institute for Mathematics in; Bonn; Max-Planck Foundation; ARC [FL170100020]; Institute for; Mathematics at the University of Potsdam; University of Adelaide;; Australian Research Council [FL170100020] Funding Source: Australian; Research Council |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| License (German): |  Keine öffentliche Lizenz: Unter Urheberrechtsschutz |
