Some results from a Mellin transform expansion for the heat kernel

Abstract

In the case of a differential operator containing a gauge field, coefficients of a new heat kernel expansion obtained in a preceding paper (A. P. C. Malbouisson, M. A. R. Monteiro, and F. R. A. Simão, CBPF-NF-024/88, to be published in J. Math. Phys.) are calculated. The prior expansion allows it to be shown that the meromorphic structure of the generalized zeta function is much richer than was known previously. Also, an application to anomalies is done, resulting in a general formula for the arbitrary dimension D. The special cases D=2 and D=3 are investigated.