Canonical quantisation in non-Abelian background fields

The canonical quantisation of Yang--Mills theory in a local background gauge is presented. The theory is shown to possess a BRS-supersymmetry, and the associated conserved charge is used to define a subsidiary condition on physical states. The Furry approximation is introduced, and an explicit example of the method in the case of a uniform external field strength is presented. The particle production rate is calculated, and the connection with the proper time formalism established. The results do not agree with those obtained by symmation of the corresponding perturbation series