Coulomb Gauge Quantization and Renormalization of the Chern–Simons Theory Coupled to Fermions

We study the quantization and the one-loop renormalization of the model resulting from the coupling of charged fermions with a Chern–Simons field, in the Coulomb gauge. A proof of the Lorentz covariance of the physical quantities follows after establishing the Dirac–Schwinger algebra for the Poincaré densities and the transformation properties of the fields under the Poincaré group. The Coulomb gauge one-loop renormalization program is, afterwards, implemented. The noncovariant form of the one-loop fermion propagator, Chern–Simons field propagator and the vertex are explicitly obtained. Finally, the electron anomalous magnetic moment is calculated stressing that, due to the peculiarities of the Coulomb gauge, the contributions from the self-energy diagrams turn out to be essential.