A variational principle for Kaluza–Klein types theories

Autor:	Frédéric Hélein
Rok vydání:	2020
Předmět:	Pure mathematics Variational principle Symmetric bilinear form General Mathematics Lie algebra Simply connected space Kaluza–Klein theory Scalar (mathematics) General Physics and Astronomy Lie group Principal bundle Mathematics
Zdroj:	Advances in Theoretical and Mathematical Physics. 24:305-326
ISSN:	1095-0753 1095-0761
DOI:	10.4310/atmp.2020.v24.n2.a3
Popis:	For any positive integer n and any Lie group G, given a definite symmetric bilinear form on R n and an Ad-invariant scalar product on the Lie algebra of G, we construct a variational problem on fields defined on an arbitrary (n + dimG)-dimensional manifold Y. We show that, if G is compact and simply connected, any global solution of the Euler-Lagrange equations leads to identify Y with the total space of a principal bundle over an n-dimensional manifold X. Moreover X is automatically endowed with a (pseudo-)Riemannian metric and a connection which are solutions of the Einstein-Yang-Mills system equation with a cosmological constant.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::06b858004bd150175b58b1b0fa9c5162 https://doi.org/10.4310/atmp.2020.v24.n2.a3 Zobrazit plný text záznamu