Supergeometry in locally covariant quantum field theory
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, o...
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| Format: | Article |
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Springer Verlag
2016
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| Online Access: | https://eprints.nottingham.ac.uk/41005/ |
| _version_ | 1848796176277569536 |
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| author | Hack, Thomas-Paul Hanisch, Florian Schenkel, Alexander |
| author_facet | Hack, Thomas-Paul Hanisch, Florian Schenkel, Alexander |
| author_sort | Hack, Thomas-Paul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions. |
| first_indexed | 2025-11-14T19:43:49Z |
| format | Article |
| id | nottingham-41005 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:49Z |
| publishDate | 2016 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410052020-05-04T17:39:28Z https://eprints.nottingham.ac.uk/41005/ Supergeometry in locally covariant quantum field theory Hack, Thomas-Paul Hanisch, Florian Schenkel, Alexander In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions. Springer Verlag 2016-03-31 Article PeerReviewed Hack, Thomas-Paul, Hanisch, Florian and Schenkel, Alexander (2016) Supergeometry in locally covariant quantum field theory. Communications in Mathematical Physics, 342 (2). pp. 615-673. ISSN 1432-0916 supergeometry algebraic quantum field theory locally covariant quantum field theory enriched category theory http://link.springer.com/article/10.1007%2Fs00220-015-2516-4 doi:10.1007/s00220-015-2516-4 doi:10.1007/s00220-015-2516-4 |
| spellingShingle | supergeometry algebraic quantum field theory locally covariant quantum field theory enriched category theory Hack, Thomas-Paul Hanisch, Florian Schenkel, Alexander Supergeometry in locally covariant quantum field theory |
| title | Supergeometry in locally covariant quantum field theory |
| title_full | Supergeometry in locally covariant quantum field theory |
| title_fullStr | Supergeometry in locally covariant quantum field theory |
| title_full_unstemmed | Supergeometry in locally covariant quantum field theory |
| title_short | Supergeometry in locally covariant quantum field theory |
| title_sort | supergeometry in locally covariant quantum field theory |
| topic | supergeometry algebraic quantum field theory locally covariant quantum field theory enriched category theory |
| url | https://eprints.nottingham.ac.uk/41005/ https://eprints.nottingham.ac.uk/41005/ https://eprints.nottingham.ac.uk/41005/ |