Approximation of the Schwinger--Dyson and the Bethe--Salpeter Equations and Chiral Symmetry of QCD
arXiv:hep-ph/9805258 · doi:10.1103/PhysRevC.59.542
Abstract
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.
10 pages, LaTex