Finite-gap integration of the SU(2) Bogomolny equations

Abstract

The ADHMN construction of magnetic monopoles is given in terms of the (normalizable) solutions of an associated Weyl equation. We focus here on solving this equation directly by algebro-geometric means. The (adjoint) Weyl equation is solved using an ans\"atz of Nahm in terms of Baker-Akhiezer functions. The solution of Nahm's equation is not directly used in our development.