We have only two possibilities to assign EW quantum numbers to the two fundamental fermion
constituents (for the general case a classification of physically relevant ultraviolet completions of composite Higgs models based on the coset SU(4)/Sp(4) is given in [56, 58], which considers different gauge groups with arbitrary numbers of flavors and colors, [N.sub.[??]] and [N.sub.HC]).
My geometrical approach with discrete symmetries alters the default reliance upon SU(2) and its continuous symmetry transformations, for I utilize discrete binary rotational subgroups of SU(2) for the fundamental fermion
states, a different subgroup for each lepton family and for each quark family.
and the RFR term is the fundamental fermion
to one photon interaction.
This means that the model under consideration does not contain exotic electric charges in the fundamental fermion
, scalar, and adjoint gauge boson representations.
The standard model identifies a dozen fundamental fermions
, or matter particles, which come in two families known as quarks and leptons.
Hence, we have proved that, for fundamental fermions
, the integral over [lambda]'s gives rise to the super-Wilson loop:
There are claims also that one cannot have more than 15 fundamental fermions
(plus 15 antifermions) without violating certain cosmological constraints.
I suggest a particular physical model of fundamental fermions based upon these finite subgroups in the discrete geometry.
These fundamental fermions and their antiparticles are defined by their electroweak isospin states in two distinct but gauge equivalent unitary planes in an internal symmetry space "attached" at a spacetime point.
In this section I combine the two Weyl [E.sub.8] groups to form a bigger group that operates in a discrete spacetime, and then in the next section I suggest a simple physical model for fundamental fermions that would fit the geometry.
A preon-based composite model of the fundamental fermions is discussed, in which the fermions are bound states of smaller entities--primitive charges (preons).
The hierarchical pattern observed in the properties of the fundamental fermions (quarks and leptons) points to their composite nature , which goes beyond the scope of the Standard Model of particle physics.