Differential regularization is used to investigate the one-loop quantum corrections to Chem-Simons-Maxwell spinor and scalar electrodynamics, We illustrate the techniques to write the loop amplitudes in coordinate space. The short-distance expansion method is developed to perform the Fourier transformation of the amplitudes into momentum space and the possible renormalization ambiguity in Chem-Simons type gauge theories in terms of differential regularization is discussed. We also stress that the surface terms appearing in the differential regularization should be kept along for finite theories and they will result in the finite renormalization ambiguity. (C) 1997 Published by Elsevier Science B.V.
