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
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.Comment: 19 Fevrier 200