Back to Cover Page

9. Conclusions.

In this paper, the F4 model has been constructed in an

8-dimensional spacetime. It has been conjectured that its extraordinary symmetry might lead to ultraviolet finiteness, but that has not been shown here.

The fermion structure corresponds naturally to the 8 fermion particles,

1 Weyl and 7 Dirac, and the 8 fermion antiparticles of the first generation. Dimensional reduction to a 4-dimensional spacetime produces the observed 3 generations of fermions.

The 28-dimensional Spin(8) gauge group reduces, in 4 dimensions, to the four gauge groups SU(3), Spin(4) = SU(2) x SU(2), U(1)4, and Spin(5).

Spin(4) = SU(2) x SU(2) reduces to the SU(2) weak force plus the Higgs mechanism.

U(1)4 reduces to the 4 covariant x, y, z, and t components of the photon.

Spin(5) reduces to gravitation by the MacDowell-Mansouri mechanism, along with the F4 model ansatz. The Spin(5) of the F4 model produces Einstein gravity, a cosmological constant term, and a surface term that is used in the quantum theory.

The F4 model calculations of force strengths, based on volumes of symmetric spaces related to gauge groups, are physically realistic:

The F4 model produces a Higgs mechanism that not only gives a realistic Lagrangian, but also gives

[ In 1998, after reading quant-ph/9806009 by Guang-jiong Ni, I realized that I made some errors in my 1992 calculation of the Higgs Vacuum Expectation Value and the Higgs mass, and I now calculate the Higgs Vacuum Expectation Value as about 260 GeV and the Higgs mass as about 145 GeV. However, I don't think that the general geometric/structural ideas were incorrect. ]

The F4 model calculations of tree-level fermion particle masses, where quark masses are constituent masses, are physically realistic:

The F4 model calculated values for quark constituent masses and lepton masses, when used with the F4 model fermion mass relationships for the Kobayashi-Maskawa parameters, give physically realistic results:

phase angle e = /2:

d s b u 0.975 0.222 -0.00461 i c -0.222 0.974 0.0423 -0.000190 i -0.0000434 i t 0.00941 -0.0413 0.999 -0.00449 i -0.00102 i


In the F4 model, radiative neutrino masses and lepton mixing according to the same Kobayashi-Maskawa parameters that apply to quarks can explain solar neutrino experimental results by a non-adiabatic MSW mechanism.


In my opinion, the qualitative and quantitative results of the F4 model justify the use of its nonstandard structures.


Back to Cover Page