Fermion Quantum Numbers and Families Replication from an Extension of Space-Time Relativity

Abstract

The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing at a space-time level the whole gauge group SO(1,3) x U(1) x SU(2) x SU(3) associated to fundamental interactions; equivalently, by assuming that internal gauge transformations are indeed local space-time transformations. The geometry naturally embodies freedoms corresponding to gravitational and non-gravitational gauge fields. As a consequence of the fact that the structural group is in part unitary, the motion of test particles gets automatically squeezed on an effective 1+3 space-time. Dimensional reduction takes place without compactification. In close analogy to the special relativistic mass-energy relation, the theory associates to every elementary particle an intrinsic energy presumably of the order of the Planck scale. The theory predicts the existence of a right-handed component of the neutrino and indicates the possibility of an extra U(1) gauge interaction.