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Abelian Duality on Globally Hyperbolic Spacetimes

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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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Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476, Potsdam, Germany

    Christian Becker & Marco Benini

  2. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, UK

    Marco Benini, Alexander Schenkel & Richard J. Szabo

  3. Maxwell Institute for Mathematical Sciences, Edinburgh, UK

    Marco Benini, Alexander Schenkel & Richard J. Szabo

  4. Higgs Centre for Theoretical Physics, Edinburgh, UK

    Marco Benini, Alexander Schenkel & Richard J. Szabo

Authors
  1. Christian Becker
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  2. Marco Benini
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  3. Alexander Schenkel
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  4. Richard J. Szabo
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Corresponding author

Correspondence to Marco Benini.

Additional information

Communicated by Y. Kawahigashi

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Becker, C., Benini, M., Schenkel, A. et al. Abelian Duality on Globally Hyperbolic Spacetimes. Commun. Math. Phys. 349, 361–392 (2017). https://doi.org/10.1007/s00220-016-2669-9

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  • DOI: https://doi.org/10.1007/s00220-016-2669-9

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