Consistent Batalin--Fradkin quantization of Infinitely Reducible First Class Constraints

TL;DR

This paper revisits the BRST quantization process for systems with infinitely reducible first class constraints, extending the phase space and explicitly constructing a finite ghost BRST charge.

Contribution

It provides a method to explicitly construct a finite ghost BRST charge for infinitely reducible constraints by extending the phase space and following a specific quantization recipe.

Findings

Explicit construction of a finite ghost BRST charge

Extension of phase space with auxiliary variables

Reaffirmation of the quantization recipe for reducible constraints

Abstract

We reconsider the problem of BRST quantization of a mechanics with infinitely reducible first class constraints. Following an earlier recipe [Phys. Lett. B 381, 105, (1996)], the original phase space is extended by purely auxiliary variables, the constraint set in the enlarged space being first stage of reducibility. The BRST charge involving only a finite number of ghost variables is explicitly constructed.