THE ROLE OF THE INTERNAL METRIC IN GENERALIZED KALUZA-KLEIN THEORIES

The dimensional reduction of a Weyl space W(N) of N = 4 + n dimensions to a principal fiber bundle P(W4,G(n)) over a four-dimensional space-time W4 with structural group G(n) of dimension n arising from the existence of n conformal Killing vector fields of the original N-metric is studied. The framework of a Weyl geometry is adopted in order to investigate conformal rescalings of the metric on the bundle P(W4, G(n)) obtained. The Weyl symmetry is then, finally, broken again by choosing a particular Weyl gauge in which the internal, i.e., fiber metric, is of constant Cartan-Killing form. This choice of gauge, yielding a Riemannian theory, forces the internal metric to play no dynamical role in the theory, as is usually assumed to be the case in non-Abelian gauge theories. However, this gauge induces a conformal transformation of the metric in the space-time base of P compared to the space-time metric obtained by the ordinary Kaluza-Klein reduction of a Riemannian space V(N). The role of vector torsion in this dimensional reduction by isometries and scale transformations is also investigated.