Topological charges in monopole theories
type: Item
instance of: scholarly article
title: Topological charges in monopole theories
zbMATH Open document ID: 0594.58051
DOI: 10.1007/BF01212532
author: J. Rawnsley
author: Peter A. Horváthy
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: Field theories with a compact, simply connected gauge group G are studied with respect to topological invariants and related conservation of charges. The theories of root systems and differential forms are used to derive the topological invariants. Spontaneous symmetry breaking through Higgs fields provides a subgroup H of G which is shown to yield a p-tuple of integer topological invariants called Higgs charges. Invariant polynomials of the Lie algebra of G homogeneous of degree p provide topological invariants which are explicitly related to these Higgs charges. From the charge operator of the Higgs field, a subgroup U(1) is constructed which leads to quantized charge. The magnetic monopole charge is determined as a linear combination of Higgs charges. The theory is illustrated for \(G=SU(n)\).
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 22E70
zbMATH DE Number: 3956066
zbMATH Keywords: topological invariants
zbMATH Keywords: Higgs charges
zbMATH Keywords: magnetic monopole
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01212532
OpenAlex ID: W2059731546
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description: scientific article; zbMATH DE number 3956066