On the construction of QED using ERG

It has been known for some time that a smooth momentum cutoff is compatible with local gauge symmetries. In this paper we show concretely how to construct QED using the exact renormalization group (ERG). First, we give a new derivation of the Ward identity for the Wilson action using the technique of composite operators. Second, parameterizing the theory by its asymptotic behavior for a large cutoff, we show how to fine-tune the parameters to satisfy the identity. Third, we recast the identity as invariance of the Wilson action under a non-linear BRST transformation.