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 |
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| 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| _version_ | 1862749037759823872 |
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| author | Ludewig, Matthias |
| author_facet | Ludewig, Matthias |
| citation_txt | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. Matthias Ludewig. SIGMA 20 (2024), 036, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T18:10:51Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212159 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:10:51Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ludewig, Matthias 2026-01-30T08:13:36Z 2024 Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. Matthias Ludewig. SIGMA 20 (2024), 036, 29 pages 1815-0659 2020 Mathematics Subject Classification: 19K56; 58J20; 81T45 arXiv:2212.02956 https://nasplib.isofts.kiev.ua/handle/123456789/212159 https://doi.org/10.3842/SIGMA.2024.036 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. I thank Ulrich Bunke for helpful discussions. It is a pleasure to thank Christian B¨ar for his continuing support over many years. I also thank the anonymous referees for their suggestions that helped improve the paper. The author is indebted to SFB 1085 “Higher Invariants” funded by the Deutsche Forschungsgemeinschaft for financial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory Article published earlier |
| spellingShingle | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory Ludewig, Matthias |
| title | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory |
| title_full | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory |
| title_fullStr | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory |
| title_full_unstemmed | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory |
| title_short | Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory |
| title_sort | categories of lagrangian correspondences in super hilbert spaces and fermionic functorial field theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212159 |
| work_keys_str_mv | AT ludewigmatthias categoriesoflagrangiancorrespondencesinsuperhilbertspacesandfermionicfunctorialfieldtheory |