COMPLEX-GEOMETRY, UNIFICATION, AND QUANTUM-GRAVITY .1. 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) --> U(3, 2)/U(3, 1) x 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.