A two-level Kaluza-Klein theory
type: Item
instance of: scholarly article
title: A two-level Kaluza-Klein theory
zbMATH Open document ID: 0633.53097
DOI: 10.1007/BF00402143
author: B. George
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The author considers a manifold P, Lie groups G and H acting on P, and pairs (\(\tau\) ',\(\tau\) '') where \(\tau\) ' is an H-invariant connection form on P fibered as a principal G-bundle over P/G and \(\tau\) '' is a G- invariant connection form on P fibered as an H-bundle over P/H. It is shown that to every pair (\(\tau\) ',\(\tau\) '') a connection form \(\mu\) in \(\rho\) (P,P/H\(\times G,H\times G)\) corresponds uniquely as well as a cross section of a vector bundle with base P/H\(\times G\). It is also shown explicitly that in the simple case \(G\times H=SU(2)\times SU(2)\) with P/H\(\times G\) identified with four-dimensional spacetime, the gauge field Lagrangian arising from the connections \(\tau\) ' and \(\tau\) '' or \(\mu\), leads to the symmetry-breaking Higgs potential.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83E15
Mathematics Subject Classification ID: 55R99
zbMATH DE Number: 4030470
zbMATH Keywords: Kaluza-Klein theory
zbMATH Keywords: dimensional reduction
zbMATH Keywords: invariant connection
reviewed by: Vanda Silveira
MaRDI profile type: Publication
cites work: Multiple fiber bundles and gauge theories of higher order
cites work: Geometry of multidimensional universes
cites work: Symmetries of Einstein-Yang-Mills fields and dimensional reduction
cites work: The role of a vector-valued field in multidimensional universe geometry
cites work: Q5731354
full work available at URL: https://doi.org/10.1007/bf00402143
OpenAlex ID: W1973278426
description: scientific article; zbMATH DE number 4030470