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Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
Matthias Ludewig Fakultät für Mathematik, Universität Regensburg, Germany
Аннотация:
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.
Ключевые слова:
Lagrangians, correspondences, functorial field theory, Clifford algebras.
Поступила: 19 мая 2023 г.; в окончательном варианте 16 апреля 2024 г.; опубликована 24 апреля 2024 г.
Образец цитирования:
Matthias Ludewig, “Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory”, SIGMA, 20 (2024), 036, 29 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma2038 https://www.mathnet.ru/rus/sigma/v20/p36
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