Removal of Chiral Anomalies in Abelian Gauge Theories

Abstract

It is shown that chiral anomalies can be removed in abelian gauge theories. After a discussion of the two dimensional case where exact solutions are available we study the four dimensional case. We use perturbation theory, i.e. analyse the triangle Feynman integrals, and determine the general expression for the divergence of the gauge current. It includes the contribution from the triangle diagram with pure vector vertices. This is essential for our argumentation. Then we show that gauges exist for which current conservation holds and the anomaly vanishes. As far as the generating functional is concerned the anomaly is employed first as gauge fixing condition. After rewriting the interaction in a gauge invariant form the gauge fixing condition can be imposed as usual. In our approach the integration over the gauge group remains trivial. By an appropriate choice of the subtraction constant referring to the triangle diagram with pure vector vertices the anomalous contributions can be made to vanish in the final expressions. In this sense the anomaly is completely spurious and a consistent quantization should be possible.