A Chiral Schwinger model, its Constraint Structure and Applications to its Quantization

TL;DR

This paper analyzes the constraint structure of the Jackiw-Rajaraman chiral Schwinger model, explores its gauge invariance via an additional scalar field, and performs canonical quantization using Dirac brackets.

Contribution

It provides a detailed constraint analysis and quantization procedure for the chiral Schwinger model, including a gauge-invariant formulation with an extra scalar field.

Findings

Constraints are explicitly derived for the model.

Gauge invariance can be restored with an additional scalar field.

Canonical quantization is achieved using Dirac brackets.

Abstract

The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.