Algebraic classification of \({\mathbb{C}}P^ n\) instanton solutions
type: Item
instance of: scholarly article
title: Algebraic classification of \({\mathbb{C}}P^ n\) instanton solutions
zbMATH Open document ID: 0533.14005
DOI: 10.1007/BF00408127
author: Roberto Catenacci
author: Cesare Reina
published in: Letters in Mathematical Physics
publication date: 1981-01-01T00:00:00Z
review text: Instanton solutions of \({\mathbb{C}}P^ n\) models defined on orientable two- dimensional Riemann surfaces \(S_ g\) are the topic of this article (g is the topologically-invariant number of handles on \(S_ g)\). Instanton solutions are defined to be harmonic maps \(\phi:S_ g\to {\mathbb{C}}P^ n\) with finite action. The harmonicity condition means that the map \(\phi\) is a local extremum of the action, and hence a solution of the equations of motion. Harmonicity therefore replaces the latter, enabling a global analysis and characterization of instantons in terms of the properties of harmonic maps to be given. It follows from standard results in algebraic geometry that instantons are rational maps, as one knows for the familiar manifolds \(E^ 2\), \(S^ 2\). Essentially, the present work is an effort toward systematic generalization of known results. Following some analysis of a general nature, the map \(\phi:S^2\to {\mathbb{C}}P^ n\) is used as an explicit illustration. The number of parameters for this \(g=0\) case is obtained. For more general manifolds, constraints on the number of instanton parameters are given. A subsequent and more detailed version of this paper was scheduled to appear.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 70Sxx
zbMATH DE Number: 3845733
zbMATH Keywords: C\(P^ n\) model
zbMATH Keywords: harmonic maps
zbMATH Keywords: rationality of instanton
zbMATH Keywords: orientable two- dimensional Riemann surfaces
reviewed by: A. A. Actor
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00408127
OpenAlex ID: W2041341108
description: scientific article; zbMATH DE number 3845733