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

TL;DR

This paper investigates the infrared properties of noncommutative QED, analyzing divergences, Lorentz violation, and the vacuum polarization, revealing a logarithmic infrared singularity linked to ultraviolet behavior.

Contribution

It provides a perturbative analysis of infrared divergences and Lorentz symmetry violation in noncommutative QED, extending understanding of its quantum corrections and anomalies.

Findings

Ultraviolet divergences are absorbable at one loop.

Infrared singularity ln(q C^T C q) is identified in vacuum polarization.

Lorentz symmetry is explicitly violated by the noncommutative structure.

Abstract

Here we examine the noncommutative counterpart of QED, which is called as noncommutative QED. The theory is obtained by examining the consistent minimal coupling to noncommutative U(1) gauge field. The *-product admits the coupling of the matter with only three varieties of charges, i.e., 0, +1 and -1. Ultraviolet divergence can be absorbed into the rescaling of the fields and the parameters at least at one loop level. To examine the infrared aspect of the theory the anomalous magnetic dipole moment is calculated. The dependence on the direction of photon momentum reflects the Lorentz symmetry violation of the system. The explicit calculation of the finite part of the photon vacuum polarization shows the singularity ln({q C^TC q}) (C^{\mu\nu} is a noncommutative parameter.) in the infrared side which also exists in noncommutative Yang-Mills theory. It is associated with the ultraviolet behavior of the theory. We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only noncommutative QED.