# Abelian duality on globally hyperbolic spacetimes

November 01, 2015

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.

open access link
doi:10.1007/s00220-016-2669-9

@article{Becker:2015ybl,
author = "Becker, Christian and Benini, Marco and Schenkel,
Alexander and Szabo, Richard J.",
title = "{Abelian duality on globally hyperbolic spacetimes}",
journal = "Commun. Math. Phys.",
volume = "349",
year = "2017",
number = "1",
pages = "361-392",
doi = "10.1007/s00220-016-2669-9",
eprint = "1511.00316",
archivePrefix = "arXiv",
primaryClass = "hep-th",
reportNumber = "EMPG-15-13",
SLACcitation = "%%CITATION = ARXIV:1511.00316;%%"
}

Keywords:

differential cohomology, Abelian gauge theory, Abelian duality, Dirac charge quantization, self-dual Abelian gauge fields