Yang-Mills-Higgs fields and harmonicity of limit maps
type: Item
instance of: scholarly article
title: Yang-Mills-Higgs fields and harmonicity of limit maps
zbMATH Open document ID: 0697.58013
author: Mitsuhiro Itoh
author: Hiroki Manabe
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: This is a preliminary announcement of a result that asserts harmonicity of the limit map \(\Phi_{\infty}\) of the Higgs field at infinity corresponding to a finite SU(2) Yang-Mills-Higgs field (A,\(\Phi)\) provided that \(\lim_{R\to \infty}\sup_{| x| \leq R}| | \Phi | (x)-1| =0\) and \(\lim_{R\to \infty}<R^ 2A(Rx),\Phi (Rx)>=0\) for all \(x\in S^ 2\). A generalization is stated replacing SU(2) by an arbitrary compact simple Lie group G. Finally, under the Donaldson correspondence, a similar argument links magnetic monopoles and holomorphic maps.
reviewed by: Gábor Tóth
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 4143076
zbMATH Keywords: harmonicity of limit maps
zbMATH Keywords: Yang-Mills-Higgs field
MaRDI profile type: Publication
full work available at URL: pjaa.65.113
OpenAlex ID: W2065855244
cites work: Instantons in two and four dimensions
cites work: Q3994593
cites work: Nahm's equations and the classification of monopoles
cites work: Restrictions on harmonic maps of surfaces
cites work: Monopoles and geodesics
cites work: On the construction of monopoles
cites work: Q3906754
DOI: 10.3792/PJAA.65.113
description: scientific article; zbMATH DE number 4143076