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Communications in Mathematical Physics

, Volume 349, Issue 1, pp 361–392 | Cite as

Abelian Duality on Globally Hyperbolic Spacetimes

  • Christian Becker
  • Marco BeniniEmail author
  • Alexander Schenkel
  • Richard J. Szabo
Article

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany
  2. 2.Department of MathematicsHeriot-Watt UniversityEdinburghUK
  3. 3.Maxwell Institute for Mathematical SciencesEdinburghUK
  4. 4.Higgs Centre for Theoretical PhysicsEdinburghUK

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