In this article, we analyze the Poincaré group as the isometry group of Minkowski space, approached here within the framework of dynamic groups. Using the work of J.M. Souriau, we investigate how the action of the group on its coadjoint orbit structure reveals physical quantities such as energy, momentum, and spin as emergent geometric entities. Extending this analysis, we incorporate antichronous transformations, thereby generalizing the group to a five-dimensional context, which geometrically encodes the presence of electric charge and the symmetry between matter and antimatter. This extension culminates in the formulation of the Janus group, which encompasses CPT symmetry. Our findings suggest that these developments initiate a geometric interpretation of Andrei Sakharov's model, wherein primordial antimatter resides within an antichronous sector of the universe, providing a novel perspective on the baryon asymmetry problem in cosmology.