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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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