On the energy of Yang-Mills fields in the presence of an external source

An expression is derived for the energy of a non-Abelian solution of the Yang-Mills equations in the presence of an external source, which permits an immediate comparison with the energy of the corresponding Coulomb-type solution. For any semisimple gauge group, a number of different field configurations are exhibited which always lead to solutions of lower energy than the Coulomb solution independent of the strength and symmetry properties of the source. The various implications of these results in view of the known instability of the Coulomb-type solution of a spherically symmetric source are discussed. (Auth.)