Minkowski Space Non-Abelian Classical Solutions with Non-Integer Winding Number Change

Abstract

Working in a spherically symmetric ansatz in Minkowski space we discover new solutions to the classical equations of motion of pure $SU(2)$ gauge theory. These solutions represent spherical shells of energy which at early times move inward near the speed of light, excite the region of space around the origin at intermediate times and move outward at late times. The solutions change the winding number in bounded regions centered at the origin by non-integer amounts. They also produce non-integer topological charge in these regions. We show that the previously discovered solutions of Luscher and Schechter also have these properties.