  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 x S_4. We explain why we
have chosen E_6 as fundamental gauge group factor and why we start with a model
with four gauge boson/fermion families to accommodate and to fit the standard
model with only three fermion families. We suggest a possible symmetry breaking
pattern of E_6^4 x S_4 that could explain quark, lepton and neutrino masses and
mixings.
