Anomalies in Quantum Field Theory

Abstract

The historically important decay of the neutral pion into two photons is re-examined using the non-operator field theory techniques of Source Theory. The equivalence of pseudoscalar and pseudovector couplings, or alternatively, the partial conservation of the axial current, is confirmed, not only for the primitive interaction, but to the next order in a. In contrast, current algebra, which initially failed to account for the pion decay, uncovered, in the analysis of non-convergent integrals, an anomaly of the axial current divergence. This saved the day at the primitive interaction level, but does not yield the a correction. The question, of vital importance for non-Abelian gauge theories, is thereby raised but not answered: Do anomalies have physical significance, or are they mathematical artifacts of a maladroit formulation?