Non-renormalizability of \theta-expanded noncommutative QED

TL;DR

This paper demonstrates that heta-expanded noncommutative QED is not renormalizable due to a divergence in the electron four-point function, but suggests potential new symmetries in the model.

Contribution

It provides a detailed one-loop divergence analysis of heta-expanded noncommutative QED and explores possible new symmetries beyond gauge and Lorentz invariance.

Findings

The model is not renormalizable due to a specific divergence.

Hints of new symmetries compatible with existing ones are identified.

Certain divergences are absent, suggesting underlying symmetries.

Abstract

Computing all divergent one-loop Green's functions of \theta-expanded noncommutative quantum electrodynamics up to first order in \theta, we show that this model is not renormalizable. The reason is a divergence in the electron four-point function which cannot be removed by field redefinitions. Ignoring this problem, we find however clear hints for new symmetries in massless \theta-expanded noncommutative QED: Four additional divergences which would be compatible with gauge and Lorentz symmetries and which are not reachable by field redefinitions are absent.