Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map

TL;DR

This paper demonstrates that the photon self-energy in noncommutative quantum electrodynamics can be renormalized at all orders using the Seiberg-Witten map, leveraging its flexibility to include necessary gauge-invariant counterterms.

Contribution

It proves all-order renormalizability of noncommutative QED photon self-energy via the Seiberg-Witten map, highlighting its role in generating divergence-canceling terms.

Findings

Photon self-energy is renormalizable to all orders.

Seiberg-Witten map's freedom allows gauge-invariant counterterms.

Divergences are compensated by field redefinitions.

Abstract

We show that the photon self-energy in quantum electrodynamics on noncommutative $\mathbb{R}^4$ is renormalizable to all orders (both in $\theta$ and $\hbar$) when using the Seiberg-Witten map. This is due to the enormous freedom in the Seiberg-Witten map which represents field redefinitions and generates all those gauge invariant terms in the $\theta$-deformed classical action which are necessary to compensate the divergences coming from loop integrations.