New Schwinger-Dyson equations for non-Abelian gauge theories

TL;DR

This paper introduces new Schwinger-Dyson equations for non-Abelian gauge theories derived via the pinch technique, which maintain gauge invariance at any truncation level and align with the background field method in Feynman gauge.

Contribution

It develops a novel non-perturbative framework using the pinch technique that produces gauge-invariant Schwinger-Dyson equations with Abelian Ward identities, streamlining calculations.

Findings

New equations exhibit gauge invariance at any truncation level

Equivalence with background field method in Feynman gauge

Framework facilitates non-perturbative analysis of gauge theories

Abstract

We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the standard case, the new series can be truncated gauge invariantly at any order in the dressed loop expansion. The construction is streamlined by resorting to the Batalin-Vilkovisky formalism which allows for a concise treatment of all the quantities appearing in the intermediate steps. The theoretical and phenomenological implications of this novel non-perturbative framework are discussed in detail.