GAUSSS LAW, GAUGE-INVARIANT STATES, AND SPIN AND STATISTICS IN ABELIAN CHERN-SIMONS THEORIES

We discuss topologically massive QED-the Abelian gauge theory in which (2+1)-dimensional QED with a Chern-Simons term is minimally coupled t o a spinor field. We quantize the theory in covariant gauges, and cons truct a class of unitary transformations that enable us to embed the t heory in a Pock space of states that implement Gauss's law. We show th at when electron (and positron) creation and annihilation operators re present gauge-invariant charged particles that are surrounded by the e lectric and magnetic fields required by Gauss's law, the unitarity of the theory is manifest, and charged particles interact with photons an d with each other through nonlocal potentials. These potentials includ e a Hopi-like interaction, and a planar analog of the Coulomb interact ion. The gauge-invariant charged particle excitations that implement G auss's law obey the identical anticommutation rules as do the original gauge-dependent ones. Rotational phases, commonly identified as plana r 'spin' are arbitrary, however.