We study the large mass asymptotics of the Dirac operator with a nondegenerate mass matrix $m=\mathrm{diag}{(m}_1{,m}_2{,m}_3)$ in the presence of scalar and pseudoscalar background fields taking values in the Lie algebra of the $\mathrm{U}\mathrm{}\left(3\right)\mathrm{}$ 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 $m_1\ne m_2\ne m_3.$ 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 $m_1{=m}_2{=m}_3.$

• Received 26 June 2001

DOI:https://doi.org/10.1103/PhysRevD.64.087701