Non Abelian gauge symmetries induced by the unobservability of extra-dimensions in a Kaluza-Klein approach

TL;DR

This paper extends the Kaluza-Klein framework to non-Abelian gauge theories, demonstrating how unobservability of extra dimensions leads to four-dimensional Einstein-Yang-Mills equations and gauge transformations.

Contribution

It shows how extra-dimensional unobservability induces non-Abelian gauge symmetries and reproduces gauge fields and transformations in a four-dimensional setting.

Findings

Reproduces Einstein-Yang-Mills equations from higher dimensions

Derives gauge transformations from extra-dimensional unobservability

Connects multidimensional matter fields to four-dimensional gauge couplings

Abstract

In this work we deal with the extension of the Kaluza-Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce fields equations and gauge transformations in the four-dimensional picture. More precisely, in fields equations any dependence on extra-coordinates is canceled out by an integration, as consequence of the unobservability of extra-dimensions. Thus, by virtue of this extra-dimensions unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein-Yang-Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang-Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.