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.
Letters in Mathematical Physics
- Pub Date:
- September 2012
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
- 23 pages, 1 figure, explicit construction of the universal algebra added in section 3