Differential cohomology and locally covariant quantum field theory

Becker, Christian and 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

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Abstract

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.

Item Type: Article
Additional Information: Electronic version of an article published as Reviews in Mathematical Physics, Volume 29, Issue 1, 2017, 1750003. doi:10.1142/S0129055X17500039 © copyright World Scientific Publishing Company. http://www.worldscientific.com/doi/abs/10.1142/S0129055X17500039
Keywords: algebraic quantum field theory, generalized Abelian gauge theory, differential cohomology
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1142/S0129055X17500039
Related URLs:
Depositing User: Schenkel, Dr Alexander
Date Deposited: 06 Mar 2017 09:30
Last Modified: 08 Dec 2017 06:01
URI: http://eprints.nottingham.ac.uk/id/eprint/41008

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