Exact solutions of the Yang-Mills equations with source in the form of two point color charges

Abstract

We find a family of exact retarded solutions of the classical Yang—Mills equations with a source that consists of two point color charges that move along arbitrary timelike worldlines in Minkowski space. The solutions are stable with respect to small field perturbations and are therefore suitable for playing the role of a nonperturbative gluon vacuum. It is shown that a description of confinement in the framework of classical Yang—Mills theory is impossible. Confinement is ensured by quantum fluctuations over the constructed gluon vacuum.