Chiral Bosons Through Linear Constraints

TL;DR

This paper investigates the quantization of a chiral boson model using linear constraints, addressing issues with indefinite metrics by introducing ghost fields and BRST symmetry, leading to a consistent physical state space.

Contribution

It presents a novel approach to quantizing chiral bosons via linear constraints and employs BRST symmetry to resolve indefinite metric issues.

Findings

The model's state space has an indefinite metric.

Ghost fields and BRST symmetry ensure physical states have zero norm.

The quartet mechanism isolates the vacuum as the only physical state.

Abstract

We study in detail the quantization of a model which apparently describes chiral bosons. The model is based on the idea that the chiral condition could be implemented through a linear constraint. We show that the space of states is of indefinite metric. We cure this disease by introducing ghost fields in such a way that a BRST symmetry is generated. A quartet algebra is seen to emerge. The quartet mechanism, then, forces all physical states, but the vacuum, to have zero norm.