  We discuss the canonical quantization of Quantum Electrodynamics in $2+1$
dimensions, with a Chern-Simons topological mass term and gauge-covariant
coupling to a Dirac spinor field. A gauge-fixing term is used which generates a
canonical momentum for $A_0$, so that there are no primary constraints on
operator-valued fields. Gauss's Law and the gauge condition, $A_0=0$, are
implemented by embedding the formulation in an appropriate physical subspace,
in which state vectors remain naturally, in the course of time evolution. The
photon propagator is derived from the canonical theory. The electric and
magnetic fields are separated into parts that reflect the presence of massive
photons, and other parts that are rigidly attached to charged fermions and do
not consist of any observable, propagating particle excitations. The effect of
rotations on charged particle states is analyzed, and the relation between the
canonical and the Belinfante ``symmetric'' angular momentum is discussed. It is
shown that the rotation operator can be consistently formulated so that charged
particles behave like fermions, and do not acquire any arbitrary phases during
rotations, even when they are dressed in the electromagnetic fields required
for them to obey Gauss's law.
