The Kugo-Ojima Confinement Criterion from Dyson-Schwinger Equations

TL;DR

This paper reviews the Kugo-Ojima confinement criterion in QCD, analyzing its derivation from Dyson-Schwinger equations and discussing the infrared behavior of propagators in Landau gauge through both theoretical and lattice approaches.

Contribution

It demonstrates how the Kugo-Ojima criterion emerges from Dyson-Schwinger equations and compares the infrared behavior of propagators from truncated equations and lattice data.

Findings

Kugo-Ojima criterion follows from ghost Dyson-Schwinger equations in Landau gauge.

Infrared behavior of propagators shows consistency between Dyson-Schwinger solutions and lattice simulations.

Positivity violations indicate confinement in transverse gluon and quark states.

Abstract

Prerequisites of confinement in the covariant and local description of QCD are reviewed. In particular, the Kugo-Ojima confinement criterion, the positivity violations of transverse gluon and quark states, and the conditions necessary to avoid the decomposition property for colored clusters are discussed. In Landau gauge QCD, the Kugo-Ojima confinement criterion follows from the ghost Dyson-Schwinger equation if the corresponding Green's functions can be expanded in an asymptotic series. Furthermore, the infrared behaviour of the propagators in Landau gauge QCD as extracted from solutions to truncated Dyson-Schwinger equations and lattice simulations is discussed in the light of these issues.