Generalized Schwinger proper time method for Dirac operator with dynamical chiral symmetry breaking

Schwinger proper time method is generalized for the calculation of real part of determinant and coincidence limit of inverse for Dirac operator with dynamical chiral symmetry breaking caused by momentum dependent fermion self energy $\mathrm{\Sigma }(k^2)$. The obtained series generalizes the heat kernel expansion for hard fermion mass.