Path integral derivation of the chiral anomalies in higher dimensional curved space-time

The gravitational contributions to the chiral U (1) anomalies for Dirac and Rarita-Schwinger fields in arbitrary even dimensions are derived on the basis of Fujikawa's path integral method. We present two methods to evaluate the Jacobian of the functional measure; the first method consists of performing the integration of the momentum representation of the heat kernel, and the second is a direct application of Schwinger's proper time method. (author)