I - Matter, antimatter and geometry II - The twin universe model : a solution to the problem of negative energy particles III - The twin universe model plus electric charges and matter-antimatter symmetry

TL;DR

This paper proposes a twin universe model based on a new dynamical group that accounts for matter-antimatter symmetry geometrically, addressing negative energy particle issues and extending to charged particles.

Contribution

It introduces a novel dynamical group framework that incorporates matter-antimatter symmetry and solves negative energy stability problems with a dual universe approach.

Findings

The model maintains energy and spin invariance under matter-antimatter symmetry.

It resolves negative energy particle stability issues.

Matter-antimatter duality is consistent in both universes.

Abstract

We introduce a new dynamical group whose coadjoint action on its momentum space takes account of matter-antimatter symmetry on pure geometrical grounds. According to this description the energy and the spin are unchanged under matter-antimatter symmetry. We recall that the antichron components of the Poincar\'{e} group, ruling relativistic motions of a mass-point particle, generate negative energy particles. The model with two twin universes, inspired by Sakharov's one, solves the stability issue. Positive and negative energy particles motions hold in two distinct folds. The model is extended to charged particles. As a result, the matter-antimatter duality holds in both universes.