Potential Energy Between Static Quarks Is Time Dependent in The Classical Yang-Mills Theory

TL;DR

This paper demonstrates that, unlike lattice QCD predictions, the classical Yang-Mills theory predicts a time-dependent potential energy between static quarks due to their time-dependent color charge, without violating energy conservation.

Contribution

It reveals that the gauge invariant potential energy between static quarks in classical Yang-Mills theory depends on time, contrasting with lattice QCD results.

Findings

Potential energy depends on time in classical Yang-Mills theory.

Time dependence arises from the quark's time-dependent color charge.

Energy conservation remains valid despite time-dependent potential.

Abstract

Lattice QCD predicts that the potential energy between static quarks is independent of time. However, in this paper we show that the gauge invariant color singlet potential energy between static quarks in the classical Yang-Mills theory depends on time even if the quarks are at rest. This is a consequence of the time dependent fundamental color charge $q^a(t)$ of the quark in the classical Yang-Mills theory. We find that the gauge invariant color singlet time dependent potential energy between static quarks does not violate the conservation of energy in the Yang-Mills theory.