Differential Regularization of Chern-Simons-Maxwell Spinor and Scalar Electrodynamics

TL;DR

This paper applies differential regularization to analyze one-loop quantum corrections in Chern-Simons-Maxwell spinor and scalar electrodynamics, highlighting the technique's handling of surface terms and renormalization ambiguities.

Contribution

It develops a coordinate space approach and a short-distance expansion method for Fourier transforming loop amplitudes in Chern-Simons gauge theories.

Findings

Demonstrates the use of differential regularization in these theories.

Identifies the role of surface terms in finite renormalization.

Discusses renormalization ambiguities specific to Chern-Simons gauge theories.

Abstract

Differential regularization is used to investigate the one-loop quantum corrections to Chern-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 Chern-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.