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

Andreas Bichl·Jesper Grimstrup·Harald Grosse·Lukas Popp·Manfred Schweda·Raimar Wulkenhaar
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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.

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Andreas Bichl, Jesper Grimstrup, Harald Grosse, Lukas Popp, Manfred Schweda, Raimar Wulkenhaar. 2001-04-25. Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map. https://doi.org/10.1088/1126-6708%2F2001%2F06%2F013

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