Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is on the question of 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 respe...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| ISSN: | 1815-0659 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212159 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. Matthias Ludewig. SIGMA 20 (2024), 036, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is on the question of 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 with a free fermionic particle in a curved spacetime.
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| ISSN: | 1815-0659 |