Differential cohomology and locally covariant quantum field theory
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology....
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| Format: | Article |
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World Scientific Publishing
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41008/ |
| _version_ | 1848796176840654848 |
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| author | Becker, Christian Schenkel, Alexander Szabo, Richard J. |
| author_facet | Becker, Christian Schenkel, Alexander Szabo, Richard J. |
| author_sort | Becker, Christian |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C*-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr\'echet-Lie group structure on differential cohomology groups. |
| first_indexed | 2025-11-14T19:43:50Z |
| format | Article |
| id | nottingham-41008 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:50Z |
| publishDate | 2017 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410082020-05-04T18:33:01Z https://eprints.nottingham.ac.uk/41008/ Differential cohomology and locally covariant quantum field theory Becker, Christian Schenkel, Alexander Szabo, Richard J. We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C*-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr\'echet-Lie group structure on differential cohomology groups. World Scientific Publishing 2017-02-28 Article PeerReviewed Becker, Christian, Schenkel, Alexander and Szabo, Richard J. (2017) Differential cohomology and locally covariant quantum field theory. Reviews in Mathematical Physics, 29 (01). 1750003/1-1750003/42. ISSN 1793-6659 algebraic quantum field theory generalized Abelian gauge theory differential cohomology http://www.worldscientific.com/doi/abs/10.1142/S0129055X17500039 doi:10.1142/S0129055X17500039 doi:10.1142/S0129055X17500039 |
| spellingShingle | algebraic quantum field theory generalized Abelian gauge theory differential cohomology Becker, Christian Schenkel, Alexander Szabo, Richard J. Differential cohomology and locally covariant quantum field theory |
| title | Differential cohomology and locally covariant quantum field theory |
| title_full | Differential cohomology and locally covariant quantum field theory |
| title_fullStr | Differential cohomology and locally covariant quantum field theory |
| title_full_unstemmed | Differential cohomology and locally covariant quantum field theory |
| title_short | Differential cohomology and locally covariant quantum field theory |
| title_sort | differential cohomology and locally covariant quantum field theory |
| topic | algebraic quantum field theory generalized Abelian gauge theory differential cohomology |
| url | https://eprints.nottingham.ac.uk/41008/ https://eprints.nottingham.ac.uk/41008/ https://eprints.nottingham.ac.uk/41008/ |