A Gauge-Invariant Color Charge in QCD

TL;DR

This paper introduces a gauge-invariant operator for color charge in QCD, demonstrating that color charge within a closed surface surrounding hadronic systems must be zero, implying these systems are color singlets.

Contribution

It defines a gauge-invariant color-charge operator in QCD and relates it to the chromoelectric field, providing insights into color confinement for hadronic systems.

Findings

Color charge operator is gauge-invariant.

Color charge enclosed by a surface surrounding hadrons must vanish.

Hadrons and nuclei are necessarily color singlets.

Abstract

A gauge-invariant color-charge operator is defined and related to an integral of the gauge-invariant chromoelectric field over a closed surface. We discuss the case of a surface all of whose points are a macroscopic distance from a system of quarks and gluons which it entirely surrounds. When this system of quarks and gluons forms a hadron or an object composed of hadrons, such as a nucleus, it is argued that the gauge-invariant color charge enclosed within this surface must vanish and the system of hadrons in the interior of the surface must be a color singlet.