BRST Quantisation of Histories Electrodynamics

TL;DR

This paper extends the classical history theory of electrodynamics with an extra component, then quantizes it using two methods—reduction and BRST extension—and shows their equivalence.

Contribution

It introduces a BRST-extended history space for electrodynamics and demonstrates the equivalence of reduced and cohomological quantum theories.

Findings

Quantization via reduction yields a consistent quantum history theory.

BRST extension provides a cohomological approach to quantization.

Both methods produce isomorphic quantum theories.

Abstract

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.