Quantum field theories on categories fibered in groupoids

Benini, Marco; Schenkel, Alexander

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 examples of homotopical quantum field theories resembling some aspects of gauge theories.

Citation

Benini, M., & Schenkel, A. (2017). Quantum field theories on categories fibered in groupoids. Communications in Mathematical Physics, 356(1), 19-64. https://doi.org/10.1007/s00220-017-2986-7

• Journal Article Type: Article
• Acceptance Date: Jul 7, 2017
• Online Publication Date: Aug 24, 2017
• Publication Date: 2017-11
• Deposit Date: Aug 21, 2017
• Publicly Available Date: Aug 24, 2017
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 356
• Issue: 1
• Pages: 19-64
• DOI: https://doi.org/10.1007/s00220-017-2986-7
• Keywords: locally covariant quantum field theory, fibered categories, Kan extension, homo-topical algebra, homotopical quantum field theory
• Public URL: https://nottingham-repository.worktribe.com/output/965351
• Publisher URL: https://link.springer.com/article/10.1007/s00220-017-2986-7
• Related Public URLs: https://arxiv.org/abs/1610.06071