Axial and vector anomalies in a broad class of invariant regularization and renormalization schemes

Within the framework of the spinor QED we describe a broad class of gauge invariant ultraviolet cut-off schemes, which provide a unifying view of the regularization of a Feynman graph in general and which may also be generalized to other gauge theories. Extending slightly this class of regularizations, we recover the standard anomalies in the axial-vector and vector Ward identities for the VVA triangle diagram. A cancellation of ultraviolet divergences for this graph is demonstrated, using an explicit-parametric representation, for a broad sub-class of our regularizations. Renormalization of the triangle graph in terms of an auxiliary soft mass is also discussed. Some earlier results concerning properties of the VVA triangle graph and perturbative aspects of the corresponding anomalies are thereby generalized considerably.We are indebted to A. Pogrebkov for numerous discussions. One of us (J. H) thanks J. Novotny for an independent check of a part of calculations.