Dynamical mechanisms for Kaluza-Klein theories

We present variational formulations of gauge theories and Einstein-Yang-Mills equations in the spirit of Kaluza-Klein theories. For gauge theories, 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 a fiber bundle structure.