Gauge boson families in grand unified theories of fermion masses: E-6(4)>< S-4

In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and undistinguishable particles of a theory of second quantization. In both cases, the permutation of these fields or particles leaves the lagrangian invariant. One can also extend the concept of family to gauge bosons. This can be obtained through the semidirect product of the gauge group with the group of permutations of n objects. In this paper we have studied the group E-6(4)>< S-4. We explain why we have chosen E6 as fundamental gauge group factor and why we start with a model with four gauge boson/fermion families to accommodate and to fit the std. model with only three fermion families. We suggest a possible symmetry breaking pattern of E-6(4)>< S-4 that could explain quark, lepton and neutrino masses and mixings.