Generalized BRST Quantization and Massive Vector Fields

TL;DR

This paper develops a generalized BRST quantization method for second class constraints, applying it to a massive vector field and deriving an effective theory similar to the Stueckelberg model, with potential for polynomial interaction massive Yang-Mills theories.

Contribution

It extends the generalized BRST quantization framework to inner product spaces and applies it to massive vector fields, proposing a new approach to massive gauge theories.

Findings

Derived an effective theory close to the Stueckelberg model.

Analyzed a simple model to extract key properties.

Suggested possibility of constructing polynomial interaction massive Yang-Mills theories.

Abstract

A previously proposed generalized BRST quantization on inner product spaces for second class constraints is further developed through applications. This BRST method involves a conserved generalized BRST charge Q which is not nilpotent but which satisfies Q=\delta+\delta^{\dagger}, \delta^2=0, and by means of which physical states are obtained from the projection \delta|ph>=\delta^{\dagger}|ph>=0. A simple model is analyzed in detail from which some basic properties and necessary ingredients are extracted. The method is then applied to a massive vector field. An effective theory is derived which is close to the one of the Stueckelberg model. However, since the scalar field here is introduced in order to have inner product solutions, a massive Yang-Mills theory with polynomial interaction terms might be possible to construct.