Path integral regularization of QED by means of Stueckelberg fields

With the help of a Stueckelberg field we construct a regularized U(1) gauge invariant action through the introduction of cutoff functions. This action has the property that it converges formally to the unregularized action of QED when the ultraviolet cutoff goes to infinity. Integrating out the Stueckelberg field exactly we obtain a regularized action, which describes the interaction of the photon with a massive screened fermion. This action is fully gauge invariant and the relation to standard QED is confirmed at the tree level and at the one loop order.