We compute explicitly the two-loop-order radiative corrections to the statistical parameter in the marginally renormalizable fermion three-dimensional Chern-Simons QED which has only the kinetic Chern-Simons term for the gauge field. Whether or not the fermion is massive, there are no infinite corrections. However, we find some finite corrections in the theory with massless fermions. We also argue that the statistical parameter is not subject to the infinite radiative corrections from the ultraviolet divergences of the theory at all orders; thus, the $\beta$ function for the statistical parameter vanishes exactly.

• Received 29 October 1992

DOI:https://doi.org/10.1103/PhysRevD.48.3918