Geometrical origin of fermion families in SU(2) × U(1) gauge theory

A spontaneously broken SU(2) × U(1) gauge theory with just one "primordial" generation of fermions is formulated in the context of generally covariant theory which contains two measures of integration in the action: the standard √-g d⁴χ and a new Φ d⁴χ, where Φ is a density built out of degrees of freedom independent of the metric. Such type of models are known to produce a satisfactory answer to the cosmological constant problem. Global scale invariance is implemented. After SSB of scale invariance and gauge symmetry it is found that with the conditions appropriate to laboratory particle physics experiments, to each primordial fermion field corresponds three physical fermionic states, Two of them correspond to particles with different constant masses and they are identified with the first two generations of the electroweak theory. The third fermionic states at the classical level get nonpolynomial interactions which indicate the existence of fermionic condensate and fermionic mass generation.