Noncommutative Dipole QED

TL;DR

This paper investigates noncommutative dipole QED with matter in the adjoint representation, calculating anomalies, beta functions, and form factors, revealing dependence on dipole direction and providing non-perturbative insights.

Contribution

It provides a detailed analysis of noncommutative dipole QED, including anomaly calculations, proof of Ward-Takahashi identity, and explicit beta function computation considering dipole direction dependence.

Findings

Axial anomaly computed in 2D and 4D using various regularizations.

Beta function depends on the dipole length direction.

Non-perturbative form factors and magnetic moment are derived.

Abstract

The noncommutative dipole QED is studied in detail for the matter fields in the adjoint representation. The axial anomaly of this theory is calculated in two and four dimensions using various regularization methods. The Ward-Takahashi identity is proved by making use of a non-perturbative path integral method. The one-loop $\beta$-function of the theory is calculated explicitly. It turns out that the value of the $\beta$-function depends on the direction of the dipole length $\vec{L}$, which defines the noncommutativity. Finally using a semi-classical approximation a non-perturbative definition of the form factors is presented and the anomalous magnetic moment of this theory at one-loop order is computed.