TY  - JOUR
A1  - Becker, Christian
A1  - Schenkel, Alexander
A1  - Szabo, Richard J.
T1  - Differential cohomology and locally covariant quantum field theory
JF  - Reviews in Mathematical Physics
N2  - 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 Fréchet–Lie group structure on differential cohomology groups.
KW  - Algebraic quantum field theory
KW  - generalized Abelian gauge theory
KW  - differential cohomology
Y1  - 2017
U6  - https://doi.org/10.1142/S0129055X17500039
SN  - 0129-055X
SN  - 1793-6659
VL  - 29
IS  - 1
PB  - World Scientific
CY  - Singapore
ER  -