The asymptotic Higgs field of a monopole
The author computes a simple asymptotic formula for the Higgs field of an SU(2)-monopole, valid up to exponentially decreasing terms: the ''algebraic'' part of the Higgs field [\textit{W. Nahm} ''Self-dual monopoles and calorons'', Bonn Univ., preprint HE-83-16]. This formula is derived from the twistor description of monopoles, and is applied to the study of boundary behaviour. This expression is harmonic, and is seen, in particular cases, to arise from a ''charge distribution'' on a union of compact disk-like surfaces in \(R^ 3\). This formula is applied to a direct proof that the boundary conditions of a monopole are satisfied when the spectral curve satisfies the conditions given by \textit{N. J. Hitchin} [Commun. Math. Phys. 83, 579-602 (1982; Zbl 0502.58017)].
scientific article; zbMATH DE number 3932071