A Semi-analytical Solution to Classic Yang-Mills Equations with Both Asymptotical Freedom and Confining Features

TL;DR

This paper presents a semi-analytical solution to classical Yang-Mills equations that exhibits both confinement and asymptotic freedom features, providing insights into non-perturbative QCD behavior at a classical level.

Contribution

It introduces a novel semi-analytical solution to classical Yang-Mills equations capturing key QCD properties like confinement and asymptotic freedom.

Findings

Solution is serial near the source and elementary at large distances.

Derived a non-perturbative beta function with linear behavior in both IR and UV.

Provides a classical model reflecting quantum-like features of QCD.

Abstract

It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics (QCD). But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang-Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the running of effective coupling constant, which is linear in the couplings both in the infrared and ultraviolet region.