Triviality of the quark propagator in the ladder approximation in QCD

TL;DR

This paper demonstrates that in QCD, the ladder approximation leads to a trivial quark propagator, highlighting its limitations and the neglect of gluon self-interactions due to the non-Abelian nature of the theory.

Contribution

It reveals that the ladder approximation in QCD results in a trivial quark propagator, emphasizing the need to consider gluon self-interactions beyond this approximation.

Findings

Ladder approximation yields a trivial quark propagator in QCD.

Color degrees of freedom impose additional constraints on SD equations.

Standard ladder approximation neglects gluon self-interactions.

Abstract

The validity of the ladder approximation (LA) in QCD and QED in the context of the corresponding Schwinger-Dyson (SD) equations and Slavnov-Taylor (ST) and Ward-Takahashi (WT) identities is investigated. In contrast to QED, in QCD bacause of color degrees of freedom the summation of the ladder diagrams within the Bethe-Salpeter (BS) integral equation for the quark-gluon vertex at zero momentum transfer on account of the corresponding ST identity does provide an an addition constraint on the quark SD equation itself. Moreover, the solution of the constraint equation requires the full quark propagator should be almost trivial (free-type) one, i. e. there is nontrivial quark propagator in the LA in QCD. This triviality results in the fact that the standard LA ignores the self-interaction between gluons caused by color charges (non-Abelian character of QCD).