Anomalies of the Axial-Vector Current

Abstract

The anomalies of the neutral axial-vector current, of its divergence, and of its commutators in the presence of electromagnetic interactions are exhibited. It is shown that it is impossible in perturbation theory to maintain minimality of electromagnetic interactions, gauge invariance, and partial conservation of axial-vector current (PCAC). The departures from gauge invariance or PCAC which are necessitated by minimality are established. The relevance of the present considerations to ${\pi }^0\to 2\gamma$ decay is discussed.