Quantization of massive vector fields on ultrastatic spacetimes

Abstract

A canonical quantization is developed for massive vector fields on ultrastatic spacetimes with compact Cauchy surfaces. At the classical level, the field equation is recast as an abstract Cauchy problem subject to a subsidiary condition. Time evolution is obtained as a unitary mapping of Cauchy data, and the subsidiary condition is satisfied by restricting the data. At the quantum level, field operators are constructed and a representation of the CCRs is obtained on a Fock space.