Gauge theories as a geometrical issue of a Kaluza-Klein framework

摘要

We present a geometrical unification theory in a Kaluza-Klein approach that achieve the geometrization of a generic gauge theory bosonic component.We show how it is possible to derive gauge charge conservation from the invariance of the model under extra-dimensional translations and to geometrize gauge connections for spinors, in order to make possible to introducing matter just through free spinorial fields. Then we present the applications to (i) a pentadimensional manifold V-4 circle times S-1 So reproducing the original Kaluza-Klein theory with some extensions related to the rule of the scalar field contained in the metric and to the introduction of matter through spinors with a phase dependance from the fifth coordinate, (ii) a seven-dimensional manifold V-4 circle times S-1 circle times S-2, in which we geometrize the electroweak model by introducing two spinors for every leptonic family and quark generation and a scalar field with two components with opposite hypercharge responsible for spontaneous symmetry breaking.