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

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.