Remark on the consistency of the ladder approximation and the rainbow approximation of Dyson-Schwinger equations of QCD

摘要

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.