BRST Quantisation of Histories Electrodynamics

This paper is a continuation of earlier work where a classical history theory of pure electrodynamics was developed in which the the history fields have \emph{five} components. The extra component is associated with an extra constraint, thus enlarging the gauge group of histories electrodynamics. In this paper we quantise the classical theory developed previously by two methods. Firstly we quantise the reduced classical history space, to obtain a reduced quantum history theory. Secondly we quantise the classical BRST-extended history space, and use the BRST charge to define a `cohomological' quantum history theory. Finally we show that the reduced history theory is isomorphic, as a history theory, to the cohomological history theory.