Abstract

In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.

Highlights

  • Gauge theories in two-space one-time dimensions involving Chern-Simons (CS) term coupled to matter fields describe excitations with fractional statistics [1,2,3,4,5,6,7,8]

  • The IF Hamiltonian, path integral and BRST formulations of this theory have been studied in Ref. [12] on the hyperplanes defined by the IF time: x0 t constant [23,24], in the broken symmetry phase of the Higgs potential [12,13,14,15] under appropriate gauge-fixing conditions

  • In this work we present the complete details of the LFQ of this theory in the broken symmetry phase of the Higgs potential

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Summary

Introduction

Gauge theories in two-space one-time dimensions involving Chern-Simons (CS) term coupled to matter fields describe excitations with fractional statistics [1,2,3,4,5,6,7,8]. The study of a theory using the IFQ as well as the LFQ determines the canonical structure and the constrained dynamics of the theory rather completely [18,19,23,24] These are the main motivations for our present studies. In this work we present the complete details of the LFQ of this theory in the broken (or frozen) symmetry phase of the Higgs potential

Light-Front Hamiltonian and Path Integral Formulations
A e2 A
A 0
Light-Front BRST Formulation
Summary and Discussion
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