Quantization of Floreanini-Jackiw chiral harmonic oscillator

TL;DR

This paper explores the path integral quantization of the Floreanini-Jackiw chiral harmonic oscillator, a constrained quantum system, using Güler's canonical formalism and Hamilton-Jacobi approach, providing insights into its gauge structure.

Contribution

It applies Güler's canonical formalism and Hamilton-Jacobi method to quantize the chiral oscillator, offering a novel approach to handling its constraints.

Findings

Path integral quantization using Güler's formalism is feasible.

All variables in this formalism are gauge variables.

The Siegel's action is derived via Hamilton-Jacobi formulation.

Abstract

The Floreanini-Jackiw formulation of the chiral quantum-mechanical system oscillator is a model of constrained theory with only second-class constraints. in the Dirac's classification.The covariant quantization needs infinite number of auxiliary variables and a Wess-Zumino term. In this paper we investigate the path integral quatization of this model using $G\ddot{u}ler's$ canonical formalism. All variables are gauge variables in this formalism. The Siegel's action is obtained using Hamilton-Jacobi formulation of the systems with constraints.