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:

• U(1) electromagnetism aE = 1/137.03608
• SU(2) weak force GF = GWmproton2  = 1.02 x 10^(-5)
• SU(3) aC=0.629 at0.24; 0.168 at 5.3; 0.122 at 34; 0.106 at 91GeV
• Spin(5) gravity GGmproton2 = (mproton/mPlanck)^2

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

• Higgs scalar mass = 260.8 GeV

• weak boson masses: mw+ = mw- = 80.9 GeV and mz = 92.4 GeV
• Weinberg angle sin2qw = 1 - (mw±/mz)^2 = 0.233.

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

• me is assumed to be 0.5110 MeV
• me-neutrino = 0; md = 312.8 MeV; mu = 312.8 MeV
• mµ = 104.8 MeV; mµ-neutrino = 0; ms =  625 MeV; mc = 2.09 GeV
• m t = 1.88 Gev; m t-neutrino = 0; mb = 5.63 GeV; mt = 130 GeV
• mPlanck (rough estimate) Å 1-1.6 x 1019 GeV.

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 = ¹/2:

       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.