Large mass invariant asymptotics of the effective action

We study the large mass asymptotics of the Dirac operator with a nondegenerate mass matrix m=diag(m₁,m₂,m₃) in the presence of scalar and pseudoscalar background fields taking values in the Lie algebra of the U(3) group. The corresponding one-loop effective action is regularized by Schwinger’s proper-time technique. Using a well-known operator identity, we obtain a series representation for the heat kernel that differs from the standard proper-time expansion, if m₁≠m₂≠m₃. After integrating over the proper time we use a new algorithm to resum the series. The invariant coefficients that define the asymptotics of the effective action are calculated up to the fourth order and compared with the related Seeley-DeWitt coefficients for the particular case of a degenerate mass matrix with m₁=m₂=m₃.