Generalized Heat Kernel Coefficients for a New Asymptotic Expansion

The method which allows for asymptotic expansion of the one-loop effective action W=ln det A is formulated. The positively defined elliptic operator A= U + M^2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nondegenerate mass matrix M=diag(m1,m2,...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley-DeWitt coefficients is clarified.