Gauge fields with respect to $d=(3+1)$ in the Kaluza-Klein theories and in the spin-charge-family theory

TL;DR

This paper demonstrates how vielbeins and spin connections in higher-dimensional theories like Kaluza-Klein and spin-charge-family theories manifest as vector gauge fields in four-dimensional space, linking geometry to gauge fields and scalar fields like the Higgs.

Contribution

It shows the equivalence of vielbeins and spin connections to gauge fields in four dimensions within symmetric higher-dimensional spaces, providing insights into the origin of gauge and scalar fields.

Findings

Vielbeins and spin connections act as gauge fields in 4D.

The equivalence holds for spaces with specific metric symmetries.

Connection between scalar gauge fields and the Higgs is discussed.

Abstract

It is shown that in the spin-charge-family theory, as well as in all the Kaluza-Klein like theories, vielbeins and spin connections manifest in $d=(3+1)$ space equivalent vector gauge fields, when space with $d\ge5$ manifests large enough symmetry. The authors demonstrate this equivalence in spaces with the symmetry of the metric tensor in the space out of $d=(3+1)$ - $g^{\sigma \tau} = \eta^{\sigma \tau} \,f^{2}$ - for any scalar function $f$ of the coordinates $x^{\sigma}$, where $x^{\sigma}$ denotes coordinates of space out of $d=(3+1)$. Also the connection between vielbeins and scalar gauge fields in $d=(3+1)$ (offering the explanation for the Higgs's scalar) is discussed.