Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917648090005504 |
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| author | Ludewig, Matthias |
| author_facet | Ludewig, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02956 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory Ludewig, Matthias Mathematical Physics Differential Geometry K-Theory and Homology 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. |
| title | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory |
| topic | Mathematical Physics Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2212.02956 |