Gauge invariant variables and the Yang-Mills-Chern-Simons theory

TL;DR

This paper performs a Hamiltonian analysis of (2+1)-dimensional Yang-Mills theory with a Chern-Simons term, revealing insights into gauge invariant variables, the mass gap, and long-distance vacuum properties.

Contribution

It introduces a gauge invariant matrix parametrization for the potentials and connects the vacuum properties to a 2D YM theory with fermions, providing new analytical tools.

Findings

Constructed gauge boson states and calculated their mass contributions.

Linked long-distance vacuum expectations to a 2D YM theory with fermions.

Compared Wilson loop expectations with previous results.

Abstract

A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level $k$ Chern-Simons term is carried out using a gauge invariant matrix parametrization of the potentials. The gauge boson states are constructed and the contribution of the dynamical mass gap to the gauge boson mass is obtained. Long distance properties of vacuum expectation values are related to a Euclidean two-dimensional YM theory coupled to $k$ flavors of Dirac fermions in the fundamental representation. We also discuss the expectation value of the Wilson loop operator and give a comparison with previous results.