Quantum field theories on categories fibered in groupoids
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 s...
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/45005/ |
| _version_ | 1848797046811656192 |
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| author | Benini, Marco Schenkel, Alexander |
| author_facet | Benini, Marco Schenkel, Alexander |
| author_sort | Benini, Marco |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:57:39Z |
| format | Article |
| id | nottingham-45005 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:57:39Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-450052020-05-04T19:54:30Z https://eprints.nottingham.ac.uk/45005/ Quantum field theories on categories fibered in groupoids Benini, Marco Schenkel, Alexander 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. Springer 2017-11 Article PeerReviewed 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 locally covariant quantum field theory fibered categories Kan extension homo-topical algebra homotopical quantum field theory https://link.springer.com/article/10.1007/s00220-017-2986-7 doi:10.1007/s00220-017-2986-7 doi:10.1007/s00220-017-2986-7 |
| spellingShingle | locally covariant quantum field theory fibered categories Kan extension homo-topical algebra homotopical quantum field theory Benini, Marco Schenkel, Alexander Quantum field theories on categories fibered in groupoids |
| title | Quantum field theories on categories fibered in groupoids |
| title_full | Quantum field theories on categories fibered in groupoids |
| title_fullStr | Quantum field theories on categories fibered in groupoids |
| title_full_unstemmed | Quantum field theories on categories fibered in groupoids |
| title_short | Quantum field theories on categories fibered in groupoids |
| title_sort | quantum field theories on categories fibered in groupoids |
| topic | locally covariant quantum field theory fibered categories Kan extension homo-topical algebra homotopical quantum field theory |
| url | https://eprints.nottingham.ac.uk/45005/ https://eprints.nottingham.ac.uk/45005/ https://eprints.nottingham.ac.uk/45005/ |