On the higher-loop contributions to the axial anomaly

Abstract

The problem of the higher-loop corrections to the axial anomaly is reexamined by a new method. We demonstrate that these contributions depend on the order in which different operations are performed. If the divergence of the axial current is calculated first, and then averaged over the photon field in the presence of an external photon source, a nonzero contribution is obtained. However the perturbative Feynman diagram method has an uncertainty. Depending on the order of the operation, one can get the above mentioned result or zero.