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Monopoles and Baker functions. (English) Zbl 0707.35128

The construction of explicit solutions of Nahm’s equations which satisfy the regularity and reality conditions required for the physical monopoles is presented. A monopole and a spectral curve (i.e. a Riemann surface) are associated together with the data of a line bundle on this curve. The bundle evolves simply, in the Nahm “time” z, on the Jacobian (a torus) of the curve. A class of elliptic solutions of Nahm’s equations for arbitrary monopole number, which correspond to singular curves with elliptic components are discussed.

This study may be used to extend the results on the dynamics of slowly moving monopoles.

35Q40PDEs in connection with quantum mechanics
81T13Yang-Mills and other gauge theories
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