Charge screening of quark sources: A gauge artefact

Abstract

Classical solutions of the SU(2) colour Yang-Mills theory with a static external source are examined subject to the following three constraints: 1. (i) all gauge-invariant quantities which may be constructed out of the gauge fields are static; 2. (ii) the colour electric fields are covariantly static; they have vanishing time derivatives in the temporal gauge; 3. (iii) a gauge exists in which the “colour direction” of the external source is a constant throughout space and time. The system is shown to possess two classes of solution. The first class consists of the familiar Coulomb solution, while members of the second class correspond to certain recently discovered “screening” solutions, with energies lower than that of the class one solution. It is shown that charge screening is not the physical mechanism underlying this result, and that for a quark source of zero total strength, the class two solutions actually have higher energies than the class one Coulomb solution. The relevance of these solutions to the problem of quark confinement and the stability of the Coulomb solution is discussed.