Ambiguity structure of the full VVA-triangle graph in 4 and n dimensions

Each of three procedures, dimensional regularization, regularization by dimensional reduction (RDR), and preregularization, are used to compute the chiral anomaly by considering the full structure of the ''un-momentum-contracted'' VVA-triangle graph. Although each procedure contains a priori a fourfold ambiguity which potentially could cancel the chiral anomaly, calculational procedures in each method reduce this to a twofold ambiguity which is insufficient to preserve simultaneously gauge invariance and the naive chiral Ward identity. The familiar chiral anomaly is obtained for each procedure. Nevertheless, RDR is problematical in that the chiral anomaly can be lost under a strict application of four-dimensional γ-matrix algebra