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The Bethe--Salpeter equation for the pion in chiral symmetric models isstudied with a special care to consistency with low-energy relations. Wepropose a reduction of the rainbow Schwinger--Dyson and the ladderBethe--Salpeter equations with a dressed gluon propagator. We prove that thereduction preserves the Ward--Takahashi identity for the axial-vector currentand the PCAC relation.Comment: 10 pages, LaTe

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