Discrete symmetries in the Kaluza-Klein-like theories

TL;DR

This paper redefines discrete symmetries in higher-dimensional Kaluza-Klein theories to ensure consistent charge and particle-antiparticle properties in four-dimensional spacetime, addressing contradictions in traditional charge conjugation.

Contribution

It introduces a new approach to discrete symmetries in higher-dimensional theories, maintaining subgroup structures and correct charge manifestations in four dimensions.

Findings

Redefinition of charge conjugation consistent with higher-dimensional symmetries.

Resolution of anti-particle spin discrepancy in Kaluza-Klein models.

Framework applicable to even-dimensional spaces.

Abstract

In theories of the Kaluza-Klein kind there are spins or total angular moments in higher dimensions which manifest as charges in the observable $d=(3+1)$. The charge conjugation requirement, if following the prescription in ($3+1$), would transform any particle state out of the Dirac sea into the hole in the Dirac sea, which manifests as an anti-particle having all the spin degrees of freedom in $d$, except $S^{03}$, the same as the corresponding particle state. This is in contradiction with what we observe for the anti-particle. In this paper we redefine the discrete symmetries so that we stay within the subgroups of the starting group of symmetries, while we require that the angular moments in higher dimensions manifest as charges in $d=(3+1)$. We pay attention on spaces with even $d$.