2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190588The 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.10 pages, LaTexHigh Energy Physics - Phenomenologytext