Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4

TL;DR

This paper analyzes the ultraviolet and infrared properties of noncommutative QED, demonstrating divergence subtraction at one loop, infrared Lorentz violation effects, and the UV/IR correlation in noncommutative Yang-Mills theory.

Contribution

It provides a perturbative analysis of divergence structures, infrared dynamics, and UV/IR mixing in noncommutative QED and Yang-Mills theories, highlighting differences from ordinary theories.

Findings

Divergences can be subtracted using standard counterterms at one loop.

Infrared effects show Lorentz symmetry violation.

UV and IR logarithmic divergences are correlated in NCYM theory.

Abstract

Here we discuss the ultraviolet and infrared aspects of the noncommutative counterpart of QED, which is called as noncommutative QED, as well as some infrared dynamics of noncommutative Yang-Mills (NCYM) theory. First we demonstrate that the divergence in the theory can be subtracted by the similar counterterms as in ordinary theory at one loop level. Then the anomalous magnetic moment is calculated to see the infrared aspect of the theory which reflects the violation of Lorentz symmetry. The evaluation of the finite part of the photon vacuum polarization shows that the logarithmically singular term in the infrared limit appears with the same weight as UV logarithmic divergence, showing the correlation between the UV and infrared dynamics in NCYM theory. NC-QED theory does not show such a property. We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only noncommutative QED.