I am principally referring to the work of Yosef Nir which I believe is listed among the references on the references page of this blog. A link is here to cover my bases.
Essentially, I am trying to get from what has already been developed on this blog to the full standard model Lagrangian (referring of course to quantum field theory). If I can show how this Lagrangian arises, I will consider myself to have constructed the standard model.
The dimensionality solutions related to a gauge field model (i.e., one based on curvature) including torsion leads to the gauge freedom (dimensionality D=0) and also sub-domains of dimensionalities D=1,2,3. This leads to the gauge fields and so the standard model gauge symmetry group SU(3)×SU(2)×U(1) pretty straightforwardly. This point is strengthened when these are related to the Poincaré group as manifested in a second tangent space, a notion stemming from the work of Strocchi. My chief frustration is that the model works to generate gauge fields and I have similarly discussed construction of Dirac fields. Yet it does not predict anything unknown so far. Admittedly, it gives a reason for exactly three field/particles generations but this is known. One could also argue it motivates the absence of right-handed neutrinos. Again, this is not actually new. So far, I am only constructing an alternate mathematical framework from which to consider the standard model. That’s hardly a bad thing, but it’s not genuinely novel either.
The five representations of the standard model fields in each generation become in this framework bases of the rotation groups within the Poincaré group. The Higgs boson becomes related to a displacement of the origin. The only thing I have not entirely worked out is the origin of the fields’ specific hypercharges. Yet, with all that, it is really just a novel perspective on the standard model. It leads to absolutely nothing beyond the standard model.
Musings on fundamental classical physics by Moshe Callen 