  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.
