Simple evaluation of chiral anomalies in the path-integral approach

We comment on the relation between Schwinger’s proper-time method and the one-dimensional supersymmetric path-integral method in the evaluation of chiral anomalies in gauge and gravitational interactions. For this purpose, we introduce a modified one-dimensional path integral which is directly related to the proper-time method by a Legendre transformation. This modified scheme provides a simple way of evaluating chiral anomalies. The one-dimensional path-integral method is also shown to work for the trace anomaly in four-dimensional flat space-time.