A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions

TL;DR

This paper develops a gauge-invariant Hamiltonian framework for non-Abelian gauge theories in (2+1) dimensions, revealing eigenstates with zero charge and a mass gap, using a matrix parametrization and WZW-action.

Contribution

It introduces a gauge-invariant matrix parametrization and computes the Jacobian via WZW-action, providing new insights into the Hamiltonian structure of non-Abelian gauge theories in lower dimensions.

Findings

Eigenstates with zero charge identified

Mass gap demonstrated in the spectrum

Gauge-invariant Hamiltonian formulation established

Abstract

The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in terms of the WZW-action for a hermitian matrix field. Some gauge-invariant eigenstates of the kinetic term of the Hamiltonian are given; these have zero charge and exhibit a mass gap.