Abelian duality on globally hyperbolic spacetimes

Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo
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