Systematic framework for generating multimonopole solutions

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Abstract
We describe a systematic framework for the construction of monopole solutions, as static self-dual gauge fields with appropriate boundary conditions, of arbitrary topological charge. This procedure is based on the Atiyah-Ward Ansatz, which is explicitly constructed and has some parameters. The solution, in general, is complex and has singularities, though it is static and has appropriate asymptotic behavior for a monopole solution. The conditions for the solution to be nonsingular and gauge transformable to a real form are given in simple algebraic form. We can then, in principle, check by explicit calculation if they are satisfied for some values of the parameters, or prove the existence of a choice of these parameters. However, we have not yet succeeded in determining these parameters besides the already known cases of one- and two-monopole solutions. We give explicit expressions for the gauge transformations and the real potentials, when these parameters can be chosen to satisfy the smoothness and reality conditions.

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