A series solution approach to monopole scattering

The dynamics of magnetic monopoles is studied Since we set up an initial value problem compatible with the slow-motion approximation, our investigation requires a thorough understanding of the static solutions. Therefore we review those aspects of SU(2) Yang-Mills-Higgs theory in (3+l)-dimensional Minkowski space-time necessary for our study, in particular, the invariance of the theory under SU(2) gauge transformation, the Bogomornyi-Prasad-Sommerfield limit, certain associated linear equations and their relation to the Riemann-Hilbert problem. We review the ansatz for n-monopole solutions which leads to the existence of a GL(2,C) gauge transformation. The construction of this transformation, which before was not given in explicit form, is our main contribution to setting-up of the initial value problem. This gauge provides analytic real solutions of the monopole equations. Our studies lead us to suitable series solutions which we use to construct a Cauchy problem guided by the idea of the slow-motion approximation. Then the existence of a unique time-dependent series solution of this problem near the origin is shown by using the Cauchy-Kowalewskyi theorem. Finally, we use Mathematica to find the leading terms of the solution which we then use to study the scattering of two monopoles Our most interesting finding is evidence of 90° scattenng