Classical Yang-Mills theory in the presence of external sources

Abstract

We study in detail the classical Yang-Mills field equations in the presence of static external sources. Their formulation as an initial-value problem in the $A_0=0\mathrm{}$ gauge provides us with a powerful tool for determining the existence of new solutions. In the case of point sources, the only static solutions known so far are the various Coulomb solutions which we classify according to their total energy and isospin. In the case of a localized but extended source, there are, besides the well-known Coulomb solution, two new types of solutions: the "magnetic dipole" solution which has the long-range behavior of a magnetic dipole field and which has lower energy than the Coulomb solution when the total external charge is large enough, and the "total screening" solution which has no long-range field strengths at all and which can have an arbitrarily low energy. We present a detailed study of these new solutions.