Geometrization of the Gauge Connection within a Kaluza-Klein Theory

TL;DR

This paper demonstrates how gauge connections in a Kaluza-Klein framework can be geometrized by extending spacetime with extra dimensions, linking gauge charges to extra-dimensional momenta, and deriving gauge couplings from the Dirac algebra structure.

Contribution

It provides a geometric interpretation of gauge couplings within Kaluza-Klein theory by relating extra-dimensional components to gauge charges and analyzing the Dirac algebra structure.

Findings

Extra-dimensional momenta correspond to gauge charges.

Gauge couplings emerge from the Dirac algebra in Kaluza-Klein spacetime.

Geometrization of gauge interactions achieved through matter fields dependence on extra coordinates.

Abstract

Within the framework of a Kaluza-Klein theory, we provide the geometrization of a generic (Abelian and non-Abelian) gauge coupling, which comes out by choosing a suitable matter fields dependence on the extra-coordinates. We start by the extension of the Nother theorem to a multidimensional spacetime being the direct sum of a 4-dimensional Minkowski space and of a compact homogeneous manifold (whose isometries reflect the gauge symmetry); we show, how on such a ``vacuum'' configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra as referred to a spacetime with the Kaluza-Klein restrictions and, by splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms outcome.