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Quantum Field Theories on Categories Fibered in Groupoids
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  • Published: 24 August 2017

Quantum Field Theories on Categories Fibered in Groupoids

  • Marco Benini  ORCID: orcid.org/0000-0003-0192-12261 &
  • Alexander Schenkel  ORCID: orcid.org/0000-0001-6790-17842 

Communications in Mathematical Physics volume 356, pages 19–64 (2017)Cite this article

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Abstract

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 toy-models of homotopical quantum field theories resembling some aspects of gauge theories.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476, Potsdam, Germany

    Marco Benini

  2. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Alexander Schenkel

Authors
  1. Marco Benini
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  2. Alexander Schenkel
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Corresponding author

Correspondence to Alexander Schenkel.

Additional information

Communicated by Y. Kawahigashi

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Benini, M., Schenkel, A. Quantum Field Theories on Categories Fibered in Groupoids. Commun. Math. Phys. 356, 19–64 (2017). https://doi.org/10.1007/s00220-017-2986-7

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  • Received: 02 November 2016

  • Accepted: 07 July 2017

  • Published: 24 August 2017

  • Issue Date: November 2017

  • DOI: https://doi.org/10.1007/s00220-017-2986-7

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