On the Consistency of the Ladder Approximation and the Rainbow Approximation of Dyson-Schwinger Equation of QCD

Details On the Consistency of the Ladder Approximation and the Rainbow Approximation of Dyson-Schwinger Equation of QCD On the Consistency of the Ladder Approximation and the Rainbow Approximation of Dyson-Schwinger Equation of QCD

2006-10-14

arxiv.org/abs/hep-ph/0610176v1

Int.J.Mod.Phys.A23:1711,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

7 pages

Scientific paper

10.1142/S0217751X08039645

We study the consistency of the ladder approximation and the rainbow approximation of the Dyson-Schwinger equation 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 exists any internal inconsistency in the usual rainbow-ladder approximation of QCD. In addition, we propose an modified ladder approximation which guarantees the Slavnov-Taylor identity for the quark-gluon vertex omitting the ghost effect in the approximation.

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