REMARK ON THE CONSISTENCY OF THE LADDER APPROXIMATION AND THE RAINBOW APPROXIMATION OF DYSON–SCHWINGER EQUATIONS OF QCD

Abstract

We study the consistency of the ladder approximation and the rainbow approximation of the Dyson–Schwinger equations of QCD. By considering the non-Abelian property of QCD, we show that the QED-type Ward–Takahashi identity is not required for the rainbow–ladder approximation of QCD. It indicates that there does not exist any internal inconsistency in the usual rainbow–ladder approximation of QCD. In addition, we propose a modified ladder approximation which guarantees the Slavnov–Taylor identity for the quark–gluon vertex omitting the ghost effect in the approximation.