  We discuss topologically massive QED --- the Abelian gauge theory in which
(2+1)-dimensional QED with a Chern-Simons term is minimally coupled to a spinor
field. We quantize the theory in covariant gauges, and construct a class of
unitary transformations that enable us to embed the theory in a Fock space of
states that implement Gauss's law. We show that when electron (and positron)
creation and annihilation operators represent gauge-invariant charged particles
that are surrounded by the electric and magnetic fields required by Gauss's
law, the unitarity of the theory is manifest, and charged particles interact
with photons and with each other through nonlocal potentials. These potentials
include a Hopf-like interaction, and a planar analog of the Coulomb
interaction. The gauge-invariant charged particle excitations that implement
Gauss's law obey the identical anticommutation rules as do the original
gauge-dependent ones. Rotational phases, commonly identified as planar `spin',
are arbitrary, however.
