Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing

Usha Kulshreshtha,James P Vary,Daya Shankar Kulshreshtha

doi:10.4236/jmp.2010.16055

Abstract

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

Highlights

Studies of the models of quantum electrodynamics in two-space one-time dimensions involving the ChernSimons (CS) theories [1,2,3,4,5,6,7,8,9,10] are of wide interest and form a rather broad field of investigations in various contexts
It may be important to mention here that because the LF coordinates are not related to the conventional IF coordinates by a finite Lorentz transformation, the descriptions of the same physical result may be different in the IF and LF dynamics and the LF quantization (LFQ) often has some advantages over the conventional IF quantization (IFQ) and a study of both the IFQ and the LFQ of a theory determines the canonical structure and constrained dynamics of a theory rather completely [8,9,10,11,12,13,14,15,16,17,18]
In the present work the theory has been quantized using the LF dynamics

Summary

Introduction

Studies of the models of quantum electrodynamics in two-space one-time dimensions involving the ChernSimons (CS) theories [1,2,3,4,5,6,7,8,9,10] are of wide interest and form a rather broad field of investigations in various contexts. It may be important to mention here that because the LF coordinates are not related to the conventional IF coordinates by a finite Lorentz transformation, the descriptions of the same physical result may be different in the IF and LF dynamics and the LF quantization (LFQ) often has some advantages over the conventional IF quantization (IFQ) and a study of both the IFQ and the LFQ of a theory determines the canonical structure and constrained dynamics of a theory rather completely [8,9,10,11,12,13,14,15,16,17,18] Different aspects of this theory have been studied by several authors in various contexts [1,2,3,4,5,6,7,8,9,10].

Hamiltonian and Path Integral Formulations

BRST Formulation

Summary and Discussion