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. 
Frederic Henry-Couannier (CPPM), Gilles D'Agostini (LAM), Jean-Pierre   Petit (LAM)