Geometrical Origin of Fermion Families in SU(2)xU(1) Gauge Theory

TL;DR

This paper presents a geometrical framework within a modified gauge theory that explains the origin of fermion families, linking them to different fermionic states emerging from a primordial fermion field after symmetry breaking.

Contribution

It introduces a covariant model with two measures of integration that naturally yields three fermionic states per primordial fermion, explaining fermion families and mass generation.

Findings

Two fermionic states correspond to known particle generations.

Third fermionic state indicates fermionic condensate formation.

Model addresses fermion family structure within gauge theory.

Abstract

A spontaneously broken SU(2)xU(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 \sqrt{-g}d^{4}x and a new \Phi d^{4}x, where \Phi 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 constant masses and they are identified with the first two generations of the electro-weak theory. The third fermionic states at the classical level get non-polynomial interactions which indicate the existence of fermionic condensate and fermionic mass generation.