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arXiv · 2201.01981

Dynamical mechanisms for Kaluza-Klein theories

Frédéric Hélein
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Abstract

We present variational formulations of gauge theories and Einstein--Yang-Mills equations in the spirit of Kaluza-Klein theories. For gaugetheories, only a topological fibration is assumed. For gravitation coupled with gauge fields, no fibration is assumed: Fields are defined on a 'space-time' $Y$ of dimension $4 + r$ without any structure a priori, where $r$ is the dimension of the structure group. If the latter is compact and simply connected, classical solutions allow to construct a manifold $X$ of dimension 4 to be the physical space-time, in such a way that $Y$ acquires the structure of a principal bundle over $X$ and leads to solutions of the Einstein--Yang-Mills systems. The special case of the Einstein-Maxwell system is also discussed: It suffices that at least one fiber closes in on a circle to deduce that the five-dimensional space-time has afiber bundle structure.

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Frédéric Hélein. 2022-01-06. Dynamical mechanisms for Kaluza-Klein theories. https://doi.org/10.1007/s11005-022-01591-6

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