Geometrizing the Anomaly

Recently a manifestly gauge invariant formalism for calculating amplitudes in quantum electrodynamics was outlined in which the field strength, rather than the gauge potential, is used as the propagating field. To demonstrate the utility of this formalism we calculate the axial and gauge anomalies explicitly in theories with both electrically and magnetically charged particles. Usually the gauge anomaly is identified as an amplitude that (in certain theories) fails to be gauge invariant, so it seems particularly enlightening to understand it in a manifestly gauge invariant formalism. We find that the three photon amplitude is still anomalous in these same theories because it depends explicitly upon the choice of the Stokes surface needed to couple the field strength to sources, so the gauge anomaly arises from geometric considerations.