Bounded orbits for classical motion of colored test particles in the Prasad-Sommerfield monopole field

A reinvestigation is given for classical motion of colored test particles in the Prasad-Sommerfield monopole field, a problem that was treated already by J. Schechter soon after the discovery of the monopole. The equation used by us can be obtained from the Wong equation if one regards the Higgs field as a component of a five dimensional translation invariant Yang-Mills potential and reinterprets the motion in the fifth direction appropriately. Its nonrelativistic limit is treated for the static, SO(3) symmetrical monopole of unit charge with SU(2) as gauge group. The total angular momentum is conserved, though the particle's mass is variable. For large distances the space motion is not simply that of an electric pole in a Dirac monopole field, as Schechter has stated neglecting the coupling to the Higgs field. The asymptotic solution at large distances proves that beyond unbounded scattering solutions there exist bounded orbits too, caused by long range forces which arise from the zero mass Higgs field. The bounded motion takes place on a closed, periodical trajectory between two meridian circles of a cone, whose axis is the total angular momentum vector. 10 refs. (author)