Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD

TL;DR

This paper introduces a gauge-invariant truncation scheme for Schwinger-Dyson equations in QCD, enabling non-perturbative analysis of the gluon self-energy while maintaining transversality even with diagram omissions.

Contribution

It proposes a novel truncation method that preserves gauge invariance at all levels of the dressed loop expansion in QCD Schwinger-Dyson equations.

Findings

Maintains transversality of gluon self-energy solutions.

Allows non-perturbative treatment with selective diagram omission.

Respects gauge invariance at any truncation level.

Abstract

We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge invariance at any level of the dressed loop expansion. When applied to the gluon self-energy, it allows for its non-perturbative treatment without compromising the transversality of the solution, even when entire sets of diagrams (most notably the ghost loops) are omitted, or treated perturbatively.