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Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Lagrangians, correspondences, functorial field theory, Clifford algebras. 
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     author = {Matthias Ludewig},
     title = {Categories of {Lagrangian} {Correspondences} in {Super} {Hilbert} {Spaces} and {Fermionic} {Functorial} {Field} {Theory}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
     volume = {20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a35/}
}
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Matthias Ludewig. Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a35/

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