Weak Riemannian structures on gauge-group orbits
type: Item
instance of: scholarly article
title: Weak Riemannian structures on gauge-group orbits
zbMATH Open document ID: 0614.58005
DOI: 10.1007/BF00669598
author: Vittorio Berzi
author: Marco Reni
published in: International Journal of Theoretical Physics
publication date: 1987-01-01T00:00:00Z
review text: Let \(\pi\) : \(P\to M\) be a principal bundle. The Sobolev extended group of gauge transformations \({\mathcal G}^{k+1}\) is a Hilbert Lie group and acts smoothly on the Sobolev extended space of connections \({\mathcal C}^ k\) (for sufficiently large k). The topological space \({\mathcal C}^ k/{\mathcal G}^{k+1}\) (which is not a smooth manifold unless one restricts oneself to irreducible connections or replaces \({\mathcal G}^{k+1}\) by \({\mathcal G}^{k+1}/center)\) admits a stratification into Hilbert manifolds; i.e. one has a countable family (\({\mathcal C}^ k_{\alpha})\) of \({\mathcal G}^{k+1}\)-invariant submanifolds and for each \(\alpha\) the orbit manifolds \({\mathcal C}^ k_{\alpha}/{\mathcal G}^{k+1}\) exist. The authors show that \({\mathcal C}^ k_{\alpha}/{\mathcal G}^{k+1}\) are (weak) Riemannian manifolds, the weak metric corresponding to the ''kinematic'' part of the Lagrangian considered in Yang-Mills theories.
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 3994586
zbMATH Keywords: gauge transformations
zbMATH Keywords: Hilbert Lie group
zbMATH Keywords: connections
zbMATH Keywords: stratification
zbMATH Keywords: Yang-Mills theories
Wikidata QID: Q115394972
reviewed by: R. Schmid
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3994586