Renormalization of Wilson Operators in Minkowski space

TL;DR

This paper discusses the renormalization process of Wilson operators in Minkowski space, highlighting unique features such as the non-trivial charge renormalization for light-like segments and the absence of extra divergences in specific smooth loops.

Contribution

It provides insights into the renormalization of Wilson operators in Minkowski space, especially regarding light-like segments and their impact on divergence structures.

Findings

Charge renormalization is non-trivial for light-like segments in Minkowski space.

Adding certain graphs restores simple charge renormalization.

Pairs of light-like separated points do not introduce additional divergences in smooth loops.

Abstract

We make some comments on the renormalization of Wilson operators (not just vacuum -expectation values of Wilson operators), and the features which arise in Minkowski space. If the Wilson loop contains a straight light-like segment, charge renormalization does not work in a simple graph-by-graph way; but does work when certain graphs are added together. We also verify that, in a simple example of a smooth loop in Minkowski space, the existence of pairs of points which are light-like separated does not cause any extra divergences.