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A variational principle for Kaluza-Klein type theories

Abstract : 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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Contributor : Frédéric Hélein Connect in order to contact the contributor
Submitted on : Tuesday, March 26, 2019 - 5:13:58 PM
Last modification on : Saturday, December 4, 2021 - 4:03:23 AM


  • HAL Id : hal-01869804, version 4
  • ARXIV : 1809.03375


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



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