Compactness theorems for coupled Yang-Mills fields
type: Item
instance of: scholarly article
title: Compactness theorems for coupled Yang-Mills fields
zbMATH Open document ID: 1067.53011
author: Xi Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-11-23T00:00:00Z
review text: The author considers the system of Young-Mills-Higgs equations (YMH equations) for the pair \((A,\Phi)\) where \(A \) is the potential of a connection in a vector bundle \(E\) over an \(n\)-dimensional manifold \(M\) with compact structure group \(G\) and \(\Phi \in \Gamma(E \otimes L)\) a Higgs field, where \(L = \text{vol}^{1/n}(M)\) is the line bundle of weight 1, which is the \(1/n\)-th power of the volume bundle. He gets two compactness theorems for solutions of this system which are generalizations of known results about pure Young-Mills equations. In particular, he proves the following theorem: Let \((A_i, \Phi_i)\) be a sequence of solutions of YMH equations. Then there exists a subsequence \((A_k, \Phi_k) \) and gauge transformations \(\sigma_k\) such that the sequence of solutions \(\sigma^*_k(A_k,\Phi_k)\) converges to a solution \((A,\Phi)\) outside a closed subset \(S\) of codimension at least 4.
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 2117740
zbMATH Keywords: coupled Young-Mills fields
zbMATH Keywords: vector bundle
zbMATH Keywords: gauge transformation
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.057
OpenAlex ID: W2063225254
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DOI: 10.1016/J.JMAA.2004.04.057
description: scientific article; zbMATH DE number 2117740