Vol. 48 (2001) REPORTS ON MATHEMATICAL PHYSICS zyxwvutsrqponmlkjihgfedcbaZYXWVU No. 3 A STUDY OF MONOPOLE SCATTERING THROUGH POWER SERIES EXPANSIONS F. ABDELWAHID and J. BURZLAFF School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland (e-mail: Jurgen.Burzlaff@dcu.ie) (Received July 5. 2000 - Revised April 5. 2001) The Ward method is used to construct initial data which correspond to two monopoles on top of each other pulled apart without any cost in potential energy. A gauge is found in which the data are real and analytic. The corresponding analytic solution near the origin is studied looking backwards and forwards in time. The solution considered breaks the combined symmetry of time inversion and 90’ rotation. Keywords: SU(2) YMH monopoles, Ward construction, time-dependent analytic solution. 1. Introduction Many methods have been used to describe the scattering of solitons in field the- ory. The most successful of the analytic techniques is the slow-motion approximation. First suggested by Manton for monopole dynamics [I, 21 it has been used also for CP” soliton scattering [3-51 and the scattering of Abelian Higgs vortices [6, 71. Numerical methods have also been applied successfully to a wide range of models. In [8], we attempted to add to the understanding of the scattering of Abelian Higgs vortices by using some other techniques. We addressed the question of global existence to put approximation techniques and numerical methods on a firmer footing. We studied the symmetries of the solution, and we used power series expansions to see explicitly what is going on at. the centre of the scattering process. This expansion technique also provided a mathematical underpinning for the numerical studies of CP’ vortex scattering [9]. In this paper we want to use the same techniques on the scattering of two SU(2) Yang-Mills-Higgs monopoles, and thus add to the body of knowledge that already exists. Our initial data, which are compatible with the slow-motion approximation, describe two monopoles sitting on top of each other; the time derivatives are given by the zero mode which corresponds to pulling the two monopoles apart. We work in a gauge in which the data are real and analytic [lo]. Questions of existence and symmetries of the solution are addressed. For our initial data an analytic solution exists near the origin. This solution breaks the combined symmetry of time inversion and 90” rotation.