IVF5. The Physical Spin ½ States

We have given the vacuum and vector boson states in terms of the more basic SU(6) spin ½ states.  To finish the specification of the physical states, we need to give the spin ½ states for quarks, electrons and neutrinos.  They will correspond to three fermion field operators acting on the vacuum.  We use the broken SU(6) symmetry of section IVF3 so that the electromagnetic and weak charges of the six creation and annihilation operators are

(IVF5-1)  

where all these basic fermion states are assumed to be zero mass.  We want the physical L and R states to be connected by the SU(6) scalar mass-generating terms of section IVF3,  and . 

If we require that all states correspond to the product of three field operators, then the operators corresponding to electrons, neutrinos and quarks are uniquely determined as

(IVF5-2a)  

(IVF5-2b)  

(IVF5-2c)  

(IVF5-2d)  

As far as we know, there is no  (which is the reason for the question mark) so that some reason must be found to account for why this state does not exist.  It is presumed that the three different generations correspond to different bound states of these triplets.  The u’s would have somewhat different bound states than the d’s, to account for intergenerational weak decays.

Even though the systematics of the SU(6) model are encouraging, a great deal of work remains to be done to fully validate the model.  The structure of the vacuum must be specified in much more detail.  The value of must be calculated and compared to experiment.  The different processes that can occur—creation and annihilation of photons or W’s, for example—must be related to the interaction term in a four-fermion Lagrangian.  And perhaps most important, one must determine whether the proper creation and annihilation of pairs can occur when each physical fermion state (quark, electron, neutrino) consists of triplets of basic fermions.