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Quantization of Maxwell’s Equations on Curved Backgrounds and General Local Covariance

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Abstract

We develop a quantization scheme for Maxwell’s equations without source on an arbitrary oriented four-dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends from a vector potential. It is shown that, in general, the associated field algebra can contain a non-trivial centre and, on account of this, such a theory cannot be described within the framework of general local covariance unless further restrictive assumptions on the topology of the spacetime are taken.

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Author notes

  1. Benjamin Lang

    Present address: Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

Authors and Affiliations

  1. Dipartimento di Fisica, Università degli Studi di Pavia & INFN Sezione di Pavia, Via Bassi 6, 27100, Pavia, Italy

    Claudio Dappiaggi

  2. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Deutschland

    Benjamin Lang

Authors
  1. Claudio Dappiaggi
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  2. Benjamin Lang
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Correspondence to Claudio Dappiaggi.

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Dappiaggi, C., Lang, B. Quantization of Maxwell’s Equations on Curved Backgrounds and General Local Covariance. Lett Math Phys 101, 265–287 (2012). https://doi.org/10.1007/s11005-012-0571-8

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  • DOI: https://doi.org/10.1007/s11005-012-0571-8

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