Fermi doublets theory

The 0 3 connection has a chiral component that seems to imply that Ti v has a chiral component, or is mixed with the chiral component of the other SU(2) chiral field of the electroweak theory. This is what happens to SU(2) electromagnetism at very high energies. It becomes very similar in formal structure to the theory of weak interactions and has implications for the theory of leptons. The electromagnetic interaction acts on a doublet that can be treated as an element of a Fermi doublet of charged leptons and their neutrinos in the SU(2) theory of the weak interaction. 

The theory so far is incomplete, however, because it has two SU(2) algebras that both act on the same Fermi spinor fields, and only one Higgs mechanism is used to compute the vacuum expectations for both fields. To improve the theory, consider that each SU(2) acts on separate spinor field doublets and that there are two Higgs fields that compute separate physical vacua for each SU(2) sector independently. The Higgs fields will give 2x2 vacuum diagonal expectations. If two entries in each of these matrices are equal, the resulting massive fermions in each of the two spinor doublets are identical. If the spin in one doublet... 

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