Canonical coordinates for Yang-Mills-Chern-Simons theory

TL;DR

This paper develops a canonical coordinate framework for 2+1-dimensional Yang-Mills-Chern-Simons theory, defining gauge covariant phase space coordinates and analyzing their Poisson structure, with implications for the theory's Hamiltonian formulation.

Contribution

It introduces gauge covariant transverse electric and magnetic field coordinates as canonical variables for the classical phase space of the theory.

Findings

Coordinates are canonically conjugate in the phase space.

Hamiltonian can be expanded as a power series in the coupling constant.

Coordinates provide a gauge covariant description of the phase space.

Abstract

We consider the classical field theory of 2+1-dimensional Yang-Mills-Chern-Simons theory on an arbitrary spatial manifold. We first define a gauge covariant transverse electric field strength, which together with the gauge covariant scalar magnetic field strength can be taken as coordinates on the classical phase space. We then determine the Poisson-Dirac bracket and find that these coordinates are canonically conjugate to each other. The Hamiltonian is non-polynomial when expressed in terms of these coordinates, but can be expanded in a power series in the coupling constant with polynomial coefficients.