Renormalization Constant of the Color Gauge Field as a Probe of Confinement

TL;DR

This paper explores how the renormalization constant of the color gauge field can serve as an indicator of confinement in quantum chromodynamics, linking gauge symmetry, asymptotic freedom, and confinement conditions.

Contribution

It demonstrates that the condition Z_3^{-1}=0 effectively signals confinement and shows this condition holds in quantum chromodynamics, connecting theoretical models with physical reality.

Findings

Z_3^{-1}=0 is a sufficient condition for confinement

The condition Z_3^{-1}=0 is satisfied in quantum chromodynamics

Features of other models follow from the confinement condition

Abstract

The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by $Z_3^{-1}=0$ where $Z_3$ denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it.