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 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.
Download full text files
SHA-1: e54eef3b6bda183f08037a2d076353dcc0164135
Additional Services
| Author details: | Marco BeniniORCiDGND, Alexander SchenkelORCiDGND |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus4-431541 |
| DOI: | https://doi.org/10.25932/publishup-43154 |
| ISSN: | 1866-8372 |
| Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
| Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (895) |
| Publication type: | Postprint |
| Language: | English |
| Date of first publication: | 2020/04/23 |
| Publication year: | 2017 |
| Publishing institution: | Universität Potsdam |
| Release date: | 2020/04/23 |
| Tag: | C-asterisk-algebra; covariance; locality; observables |
| Issue: | 895 |
| Number of pages: | 48 |
| Source: | Communications in Mathematical Physics 356 (2017) pp. 19-64 DOI: 10.1007/s00220-017-2986-7 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
| Peer review: | Referiert |
| Publishing method: | Open Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
| External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |
