  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 $\L_R > 0$.
We prove, using the flow equation technique, that infrared convergence is a
necessary consequence of any zero-momentum renormalization condition at $\L_R$
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.
