Quantum field theories on categories fibered in groupoids

Benini, Marco and Schenkel, Alexander (2017) Quantum field theories on categories fibered in groupoids. Communications in Mathematical Physics, 356 (1). pp. 19-64. ISSN 1432-0916

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We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first examples of homotopical quantum field theories resembling some aspects of gauge theories.

Item Type: Article
Keywords: locally covariant quantum field theory, fibered categories, Kan extension, homo-topical algebra, homotopical quantum field theory
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s00220-017-2986-7
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Depositing User: Eprints, Support
Date Deposited: 21 Aug 2017 08:34
Last Modified: 16 Nov 2017 17:53
URI: http://eprints.nottingham.ac.uk/id/eprint/45005

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