Analytic structure of the Landau gauge gluon propagator

TL;DR

This paper investigates the non-perturbative analytic structure of the gluon propagator in Landau gauge Yang-Mills theory using Dyson-Schwinger equations, revealing a cut structure and positivity violation that imply gluons are not part of the physical spectrum.

Contribution

It provides a detailed numerical analysis of the gluon and ghost propagators' analytic structure in the complex momentum plane, confirming the absence of gluons from the physical spectrum.

Findings

Gluon and ghost propagators are analytic except for a cut on the real axis.

The gluon propagator violates positivity, indicating gluons are not physical particles.

The study supports the confinement of gluons in Yang-Mills theory.

Abstract

The analytic structure of the non-perturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.