Differential cohomology and locally covariant quantum field theory

Understand

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.