The asymptotic Higgs field of a monopole
type: Item
instance of: scholarly article
title: The asymptotic Higgs field of a monopole
zbMATH Open document ID: 0582.58040
DOI: 10.1007/BF01213404
author: Jacques Hurtubise
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 3932071
zbMATH Keywords: asymptotic Higgs field
zbMATH Keywords: harmonic
zbMATH Keywords: quaternionic structure
zbMATH Keywords: Bogomolny equations
zbMATH Keywords: SU(2)-monopole
zbMATH Keywords: monopoles
zbMATH Keywords: spectral curve
reviewed by: Michael Th. Rassias
MaRDI profile type: Publication
cites work: Monopoles and geodesics
cites work: On the construction of monopoles
cites work: \(\text{SU}(2)\) monopoles of charge \(2\)
cites work: Q4195061
description: scientific article; zbMATH DE number 3932071