Non-perturbative constraints on the quark and ghost propagators

TL;DR

This paper derives non-perturbative constraints on quark and ghost propagators in QCD, revealing spectral densities with discrete mass components and singularities related to confinement.

Contribution

It explicitly establishes non-perturbative constraints on the analytic structure of quark and ghost propagators in QCD, including spectral densities and singular contributions.

Findings

Spectral densities include discrete mass components.

Propagators can contain derivatives of δ(p) terms.

Constraints are relevant for understanding confinement.

Abstract

In QCD both the quark and ghost propagators are important for governing the non-perturbative dynamics of the theory. It turns out that the dynamical properties of the quark and ghost fields impose non-perturbative constraints on the analytic structure of these propagators. In this work we explicitly derive these constraints. In doing so we establish that the corresponding spectral densities include components which are multiples of discrete mass terms, and that the propagators are permitted to contain singular contributions involving derivatives of $\delta(p)$, both of which are particularly relevant in the context of confinement.