On the construction of monopoles for the classical groups
type: Item
instance of: scholarly article
title: On the construction of monopoles for the classical groups
zbMATH Open document ID: 0682.32026
DOI: 10.1007/BF01221407
author: Michael K. Murray
author: Jacques Hurtubise
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: In recent years, magnetic monopoles have been extensively studied in at least three different ways, namely by a direct analytic approach, by twistor methods and by an extension, due to W. Nahm, of the ADHM construction for instantons. In the case when the gauge groups is SU(2), a detailed account of these methods and the relationship between them has been given by \textit{N. J. Hitchin} [Commun. Math. Phys. 83, 579-602 (1982; Zbl 0502.58017); ibid. 89, 145-190 (1983; Zbl 0517.58014)]. The object of this paper is to extend these ideas to the other classical groups, establishing in each case an equivalence between three types of data, namely (A) generic monopoles with maximum symmetry breaking at infinity, (B) generic solutions of Nahm's equations satisfying appropriate boundary conditions and (C) spectral data.
Mathematics Subject Classification ID: 32L25
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 20G45
zbMATH DE Number: 4116940
zbMATH Keywords: spectral curve
zbMATH Keywords: Nahm's equation
zbMATH Keywords: monopoles
zbMATH Keywords: twistor
zbMATH Keywords: gauge groups
Wikidata QID: Q55968622
reviewed by: P. E. Newstead
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01221407
OpenAlex ID: W2077895993
description: scientific article; zbMATH DE number 4116940