Covariance of the gauge field in three-dimensional quantum electrodynamics

We consider a theory of electrodynamics in three-dimensional space-time in the presence of the topological (Chern-Simons) interaction term (κ/2)εμνρAμ∂νAρ. It is appropriate to quantize electrodynamics in the radiation gauge because in that gauge the states in the Hilbert space have positive-definite norms. However, in that gauge the vector potential Aμ cannot transform as a vector under the Lorentz group. We show that the vector potential does transform covariantly as a representation of the Lorentz group, but the representation is infinite dimensional and, surprisingly, the specific representation depends on the value of the parameter κ