Hilbert Space of Isomorphic Representations of Bosonized Chiral $QCD_2$

TL;DR

This paper investigates the Hilbert space structure of different formulations of chiral QCD2, revealing limitations of BRST conditions and emphasizing the role of superselection rules and constraint structures.

Contribution

It provides a detailed analysis of the Hilbert space and constraint structure of bosonized chiral QCD2 at a specific parameter value, highlighting the need for superselection rules.

Findings

BRST conditions are insufficient for defining physical states.

Superselection rules are necessary in the Hilbert space.

Primary constraints are of first class in the gauge invariant formulation.

Abstract

We analyse the Hilbert space structure of the isomorphic gauge non-invariant and gauge invariant bosonized formulations of chiral $QCD_2$ for the particular case of the Jackiw-Rajaraman parameter $ a = 2$. The BRST subsidiary conditions are found not to provide a sufficient criterium for defining physical states in the Hilbert space and additional superselection rules must to be taken into account. We examine the effect of the use of a redundant field algebra in deriving basic properties of the model. We also discuss the constraint structure of the gauge invariant formulation and show that the only primary constraints are of first class.