Analysis of inter-quark interactions in classical chromodynamics

TL;DR

This paper develops an approximate method to analyze inter-quark interactions in classical chromodynamics by reformulating the QCD Lagrangian with the gluon propagator, providing insights into their static, non-relativistic behavior.

Contribution

It introduces a reformulation of the QCD Lagrangian incorporating the gluon propagator explicitly, offering a new perspective on inter-quark interactions in classical chromodynamics.

Findings

Derived the coordinate-space form of inter-quark interactions

Analyzed the static, non-relativistic interaction behavior

Provided a framework for approximate solutions of the gluon equation of motion

Abstract

The QCD gluon equation of motion is solved approximately by means of the Green function. This solution is used to reformulate the Lagrangian of QCD such that the gluon propagator appears directly in the interaction terms of the Lagrangian. The nature of the interactions is discussed. Their coordinate-space form is presented and analyzed in the static, non-relativistic case.