COULOMB GAUGE QUANTIZATION OF THE MAXWELL-CHERN-SIMONS THEORY

The Maxwell-Chern-Simons theory is canonically quantized in the Coulom b gauge by using the Dirac bracket quantization procedure. The determi nation of the Coulomb gauge polarization vector turns out to be intric ate. A set of quantum Poincare densities obeying the Dirac-Schwinger a lgebra and, therefore, free of anomalies is constructed. The peculiar analytical structure of the polarization vector is shown to be at the root for the existence of spin of the massive gauge quanta. The Coulom b gauge Feynman rules are used to compute the Moller scattering amplit ude in the lowest order of perturbation theory. The result coincides w ith that obtained by using covariant Feynman rules. This proof of equi valence is afterwards extended to all orders of perturbation theory. T he so-called infrared safe photon propagator emerges as an effective p ropagator which allows for replacing all the terms in the interaction Hamiltonian of the Coulomb gauge by the standard field-current minimal interaction. (C) 1995 Academic Press, Inc.