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arXiv · 2212.02956

Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory

Matthias Ludewig
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Abstract

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.

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Matthias Ludewig. 2022-12-06. Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. https://doi.org/10.3842/sigma.2024.036

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