MONOPOLE SCATTERING WITH A TWIST

By imposing certain combined inversion and rotation symmetries on the rational, maps for SU(2) BPS monopoles we construct geodesics in the m onopole moduli space. In the moduli space approximation these geodesic s describe a novel kind of monopole scattering, During these scatterin g processes axial symmetry is instantaneously attained and, in some, m onopoles with the symmetries of the regular solids are formed. The sim plest example corresponds to a charge three monopole invariant under a combined inversion and 90 degrees rotation symmetry. In this example three well-separated collinear unit charge monopoles coalesce to form first a tetrahedron, then a torus, then the dual tetrahedron and final ly separate again along the same axis of motion. We explicitly constru ct the spectral curves in this case and use a numerical ADHMN construc tion to compute the energy density at various times during the motion. We find that the dynamics of the zeros of the Higgs field is extremel y rich and we discover a new phenomenon; there exist charge k SU(2) BP S monopoles with more than k zeros of the Higgs held.