Quantization of the electromagnetic field on static space–times

Abstract

A quantization of the electromagnetic four-potential in the Lorentz gauge on static space–times with compact Cauchy surfaces is developed herein. For the classical problem, the field solution is obtained by use of a Hilbert space approach in which time evolution reduces to a unitary mapping of Cauchy data. For the quantum problem, a representation of the CCRs on a Fock space is constructed. The gauge condition is imposed as a constraint on state vectors and determines a physical subspace. The field equations are recovered on the physical Fock space (Gupta–Bleuler method).