Renormalizability Proof for QED Based on Flow Equations

We prove the perturbative renormalizability of Euclidean QED4 using flow equations, i.e. with the aid of the Wilson renormalization group adapted to perturbation theory. As compared to Φ44 the additional difficulty to overcome is that the regularization violates gauge invariance. We prove that there exists a class of renormalization conditions such that the renormalized Green functions satisfy the QED Ward identities and such that they are infrared finite at nonexceptional momenta. We give bounds on the singular behaviour at exceptional momenta (due to the massless photon) and comment on the adaptation to the case when the fermions are also massless. (orig.)