Classical Solutions of Yang-Mills-Theory

Abstract

In this lecture I shall present a review on classical, static solutions of the Yang-Mills field equations in presence of charge- and current sources, I shall consider only the SU(2) theory and concentrate essentially on solutions describing spherically symmetric situations. Thus the solutions to be discussed can be considered as the simplest non-Abelian generalization of the well known Coulomb-Biot-Savart solution in classical electrodynamics. The idea behind studying classical solutions is that investigations in quantum theory should perhaps not be performed without any reference to the classical theory (though the relation between classical and quantum mechanics may differ in Abelian and non-Abelian theories). In addition, some peculiar features on non-Abelian theories can be studied already on the classical level.