Fermion families and long-range force problems: Interrelation and resolution

We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard √d⁴x and a new φd⁴x, where φ is a density built out of degrees of freedom independent of the metric. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.