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

TL;DR

This paper develops a geometrical unification of gauge theories within a Kaluza-Klein framework, deriving gauge charge conservation and geometrizing gauge connections, with applications to extended manifolds including models of electroweak symmetry breaking.

Contribution

It introduces a novel geometrical approach to unify gauge theories with gravity using extended Kaluza-Klein manifolds, incorporating matter fields as spinors.

Findings

Derived gauge charge conservation from extra-dimensional invariance.

Geometrized gauge connections for spinors.

Applied to models including the original Kaluza-Klein and electroweak unification.

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.