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

F. Cianfrani·A. Marrocco·G. Montani
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Abstract

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 the gauge charge conservation from the invariance of the model under extra-dimensional translations and to geometrize gauge connections for spinors, thus we can introduce the matter just by free spinorial fields. Then, we present the applications to i)a pentadimensional manifold $V^{4}\otimes S^{1}$, so reproducing the original Kaluza-Klein theory, unless some extensions related to the rule of the scalar field contained in the metric and the introduction of matter by spinors with a phase dependence from the fifth coordinate, ii)a seven-dimensional manifold $V^{4}\otimes S^{1}\otimes S^{2}$, in which we geometrize the electro-weak model by introducing two spinors for any leptonic family and quark generation and a scalar field with two components with opposite hypercharge, responsible of spontaneous symmetry breaking.

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F. Cianfrani, A. Marrocco, G. Montani. 2005-11-11. Gauge theories as a geometrical issue of a Kaluza-Klein framework. https://doi.org/10.1142/s0218271805006900

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