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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Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2024
Автор: Ludewig, Matthias
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2024
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/212159
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. Matthias Ludewig. SIGMA 20 (2024), 036, 29 pages

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
Резюме: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.
ISSN:1815-0659