Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase

Usha Kulshreshtha, Daya S. Kulshreshtha, James P. Vary

Department of Physics and Astronomy, Iowa State University, Ames, USA.
Department of Physics and Astrophysics, University of Delhi, Delhi, India.
Department of Physics, Kirori Mal College, University of Delhi, Delhi, India.

DOI: 10.4236/jmp.2013.44A007                

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(x^μ) of the complex matter field Φ(x^μ) 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.

Keywords

Light-Front Quantization; Hamiltonian Quantization; Path Integral Quantization; BRST Quantization; Constrained Dynamics; Gauge Symmetry; Chern-Simons-Higgs Theory; Broken Symmetry Phase; Higgs Potential; Spontaneous Symmetry Breaking

Conflicts of Interest

The authors declare no conflicts of interest.

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