Treatment of a System with Explicitly Broken Gauge Symmetries

TL;DR

This paper explores how to quantize a system with explicitly broken gauge symmetry using the Dirac constraint formalism, demonstrated through a model involving an antisymmetric tensor and a spinor field.

Contribution

It introduces a method to handle systems with broken gauge symmetries during quantization, using a specific example with Dirac constraints.

Findings

Successfully applies Dirac formalism to a broken gauge symmetry system

Provides a framework for quantizing systems with explicit gauge symmetry breaking

Illustrates the approach with a tensor-spinor interaction model

Abstract

A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty by considering an antisymmetric tensor field interacting with a spinor field.