Extravariables in the BRST Quantization of Second-Class Constrained Systems; Existence Theorems

TL;DR

This paper demonstrates how BRST quantization can be extended to second-class constrained systems by converting them into first-class systems with extravariables, ensuring consistent path integral formulations.

Contribution

It introduces a method to convert second-class systems into first-class ones using extravariables, enabling standard BRST quantization and path integral equivalence.

Findings

Existence of a standard coupling for certain second-class systems

Path integral equivalence between original and converted systems

Explicit derivation of Wess-Zumino action

Abstract

In this paper we show how the BRST quantization can be applied to systems possessing only second-class constraints through their conversion to some first-class ones starting with our method exposed in [Nucl.Phys. B456 (1995)473]. Thus, it is proved that i) for a certain class of second-class systems there exists a standard coupling between the variables of the original phase-space and some extravariables such that we can transform the original system into a one-parameter family of first-class systems; ii) the BRST quantization of this family in a standard gauge leads to the same path integral as that of the original system. The analysis is accomplished in both reducible and irreducible cases. In the same time, there is obtained the Lagrangian action of the first-class family and its provenience is clarified. In this context, the Wess-Zumino action is also derived. The results from the theoretical part of the paper are exemplified in detail for the massive Yang-Mills theory and for the massive abelian three-form gauge fields.