Canonical quantization of spontaneously broken topologically massive gauge theory

TL;DR

This paper develops the canonical quantization framework for a non-Abelian topologically massive gauge theory with spontaneous symmetry breaking, analyzing particle content, propagators, and Lorentz transformations.

Contribution

It introduces a canonical operator structure for the partially broken non-Abelian Chern-Simons-Higgs model, detailing the particle spectrum and dynamical generators.

Findings

Constructed the Fock space for the theory.

Derived propagators for gauge and scalar fields.

Demonstrated Lorentz boost effects on particle states.

Abstract

In this paper we investigate the canonical quantization of a non-Abelian topologically massive Chern-Simons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Such a model produces the Chern-Simons-Higgs mechanism in which the gauge excitations acquire mass both from the Chern-Simons term and from the Higgs-Kibble effect. The symmetry breaking is chosen to be only partially broken, in such a way that in the broken vacuum there remains a residual non-Abelian symmetry. We develop the canonical operator structure of this theory in the broken vacuum, with particular emphasis on the particle-content of the fields involved in the Chern-Simons-Higgs mechanism. We construct the Fock space and express the dynamical generators in terms of creation and annihilation operator modes. The canonical apparatus is used to obtain the propagators for this theory, and we use the Poincar\'e generators to demonstrate the effect of Lorentz boosts on the particle states.