Complex geometry, unification, and quantum gravity. I : The geometry of elementary particles

The Poincare group is replaced by U(3,2), the pseudounitary extension of the de Sitter group SO(3,2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundle U(3,2) [yields] U(3,2)/U(3,1) [times] U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.