  We study generalized electric/magnetic duality in Abelian gauge theory by
combining techniques from locally covariant quantum field theory and
Cheeger-Simons differential cohomology on the category of globally hyperbolic
Lorentzian manifolds. Our approach generalizes previous treatments using the
Hamiltonian formalism in a manifestly covariant way and without the assumption
of compact Cauchy surfaces. We construct semi-classical configuration spaces
and corresponding presymplectic Abelian groups of observables, which are
quantized by the CCR-functor to the category of $C^*$-algebras. We demonstrate
explicitly how duality is implemented as a natural isomorphism between quantum
field theories. We apply this formalism to develop a fully covariant quantum
theory of self-dual fields.
