Gauge invariance, the quantum action principle, and the renormalization group

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We show that an effective quantum action principle can be formulated in perturbation theory which enables the effective Ward identities to be solved order by order, even if the theory requires nonvanishing subtraction points. The difficulties encountered with nonperturbative approximations are briefly discussed.