Large Mass Invariant Asymptotics of the Effective Action

Abstract

We study the large mass asymptotics of the Dirac operator with a nondegenerate mass matrix m={diag}(m_1,m_2,m_3) 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 the Schwinger's proper-time technique. Using a well-known operator identity, we obtain a series representation for the heat kernel which 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 which 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.