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

Lei Chang·Yu-xin Liu
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Abstract

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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Lei Chang, Yu-xin Liu. 2006-10-14. On the Consistency of the Ladder Approximation and the Rainbow Approximation of Dyson-Schwinger Equation of QCD. https://doi.org/10.1142/s0217751x08039645

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