A non-perturbative, semi-classical approach to the calculation of the quark force

A non-perturbative, semi-classical method for the calculation of the effective potential between heavy quarks is here proposed. The technique we present is a minimal extension of the classical Yang-Mills equations to operator equations in the space of isospin states of a static quark-antiquark pair. We obtain a set of non-linear partial differential equations which, when expanded in perturbation theory and improved by the renormalization group, reproduce to within 1% accuracy the order α³ QCD result for the potential.