A new perturbative derivation of the axial anomaly

Abstract

We examine the anomalous VVA and AAA three-point functions by using a perturbative expansion due to Schwinger in place of the usual Feynman diagramatic expansion. Using dimensional regularization, we show that the usual anomaly in the divergence of the axial current is automatically obtained if γ5 is treated naively (i.e., γ5 anticommutes with all γμ in n dimensions); no extra contributions occur even if γ5 is defined according to the ′t Hooft–Veltman prescription. Furthermore, no explicit divergences occur in our computation of VVA and AAA.