Approximation of the Schwinger-Dyson and the Bethe-Salpeter equations and chiral symmetry of QCD

The Bethe-Salpeter equation for the pion in chiral symmetric models is studied with a special care to consistency with low-energy relations. We propose a reduction of the rainbow Schwinger-Dyson and the ladder Bethe-Salpeter equations with a dressed gluon propagator. We prove that the reduction preserves the Ward-Takahashi identity for the axial-vector current and the PCAC relation.