Non-renormalizability of θ-expanded noncommutative QED

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.