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The fermionic integral on loop space and the Pfaffian line bundle.
- Source :
-
Journal of Mathematical Physics . Dec2022, Vol. 63 Issue 12, p1-26. 26p. - Publication Year :
- 2022
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIFFERENTIAL forms
*PATH integrals
*INTEGRALS
*ALGEBRA
*FINITE, The
Subjects
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 63
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 161087404
- Full Text :
- https://doi.org/10.1063/5.0060355