Ludewig, Matthias (2024) Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 20: 036. ISSN 1815-0659,
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In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian. Our answer leads in particular to a well-defined composition law in a category of Lagrangian correspondences respecting given polarizations of the Hilbert spaces involved. As an application, we construct a functorial field theory on geometric spin manifolds with values in this category of Lagrangian correspondences, which can be viewed as a formal Wick rotation of the theory associated to a free fermionic particle in a curved spacetime.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Lagrangians; correspondences; functorial field theory; Clifford algebras |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Jul 2025 06:59 |
| Last Modified: | 17 Jul 2025 06:59 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63402 |
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