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Pré-Publication, Document De Travail Année : 2019

A variational principle for Kaluza-Klein type theories

Résumé

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.
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Dates et versions

hal-01869804 , version 1 (06-09-2018)
hal-01869804 , version 2 (15-10-2018)
hal-01869804 , version 3 (25-10-2018)
hal-01869804 , version 4 (26-03-2019)

Identifiants

Citer

Frédéric Hélein. A variational principle for Kaluza-Klein type theories. 2019. ⟨hal-01869804v4⟩
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