Canonical coordinates for Yang-Mills-Chern-Simons theory

Abstract

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.

Keywords

• Field Theories in Lower Dimensions
• Chern-Simons Theories