Quantization of Maxwell's equations on curved backgrounds and general local covariance

TL;DR

This paper develops a quantization scheme for Maxwell's equations on curved spacetimes, highlighting the role of the field strength tensor and the impact of spacetime topology on the algebraic structure.

Contribution

It introduces a novel quantization approach that does not rely on a vector potential and analyzes the algebraic structure's dependence on spacetime topology.

Findings

Field algebra can have a non-trivial centre.

Quantization cannot be fully covariant without topological restrictions.

The field strength tensor is central to the quantization scheme.

Abstract

We develop a quantization scheme for Maxwell's equations without source on an arbitrary 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 made.