ZERO MODES OF ROTATIONALLY SYMMETRICAL GENERALIZED VORTICES AND VORTEX SCATTERING

Zero modes of rotationally symmetric vortices in a hierarchy of genera lized Abelian Higgs models are studied. Under the finite energy and th e smoothness condition, it is shown, that in all models, n self-dual v ortices superimposed at the origin have 2n modes. The relevance of the se modes for vortex scattering is discussed: first, in the context of the slow-motion approximation; second, a corresponding Cauchy problem for an all head-on collision of n vortices is formulated. It is shown that the solution of this Cauchy problem has a pi/n symmetry. (C) 1996 American Institute of Physics.