DIRAC QUANTIZATION OF THE CHERN-SIMONS FIELD-THEORY IN THE COULOMB GAUGE

In this letter the Chern-Simons field theories are studied in the Coul omb gauge using the Dirac's canonical formalism for constrained system s. As a strategy, we first work out the constraints and then quantize, replacing the Dirac brackets with quantum commutators. We find that t he Chern-Simons field theories become two dimensional models with no p ropagation along the time direction. Moreover, we prove that, despite of the presence of non-trivial self-interactions in the gauge fixed fu nctional, the commutation relations between the fields are trivial at any order in perturbation theory in the absence of couplings with matt er fields. If these couplings are present, instead, the commutation re lations become rather involved, but it is still possible to study thei r main properties and to show that they vanish at the tree level. (C) 1997 Elsevier Science B.V.