Hard-soft renormalization and the exact renormalization group

Abstract The Wilsonian exact renormalization group gives a natural framework in which ultraviolet and infrared divergences can be treated separately. In massless QED we introduce, as the only mass parameter, a renormalization scale Λ R 0. We prove, using the flow equation technique, that infrared convergence is a necessary consequence of any zero-momentum renormalization condition at Λ R compatible with the effective Ward identities and axial symmetry. The same formalism is applied to renormalize gauge-invariant composite operators and to prove their infrared finiteness; in particular we consider the case of the axial current operator and its anomaly.