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

Abstract

We show that the photon self-energy in quantum electrodynamics on noncommutative $\mathbb{R}^4$ is renormalizable to all orders (both in $θ$ 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 $θ$-deformed classical action which are necessary to compensate the divergences coming from loop integrations.

12 pages, LaTeX2e. v3: added references, changed title. The general renormalizability proof for noncommutative Maxwell theory turned out to be incomplete, therefore, we have to restrict the proof to the noncommutative photon self-energy