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arXiv · 1511.00316

Abelian duality on globally hyperbolic spacetimes

Christian Becker·Marco Benini·Alexander Schenkel·Richard J. Szabo
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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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Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo. 2016-06-15. Abelian duality on globally hyperbolic spacetimes. https://doi.org/10.1007/s00220-016-2669-9

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