To build the F4 model, the 27-dimensional exceptional Jordan algebra H3(O) is used to construct a single-particle state space of a quantum theory. The 54-dimensional complexification of H3(O) is used to construct the Fock space of a quantum field theory. The Lagrangian gauge field structure of the theory can be described in terms of the automorphism group of H3(O), the 52-dimensional exceptional Lie group F4, after which the F4 model is named.
F4 is made up of the 28-dimensional adjoint representation Ad28 of Spin(8), the 8-dimensional vector representation V8 of Spin(8), and the two mirror image 8-dimensional half-spinor representations S8+ and S8- of Spin(8).
The F4 model uses Ad28 as the Lie algebra of the gauge group Spin(8),
V8 as an 8-dimensional tangent vector space of spacetime,
S8+ as 8 fermion particles (neutrino, red up quark, green up quark, blue up quark, red down quark, green down quark, blue down quark, and electron), and S8- as 8 fermion antiparticles, with physics defined by the Lagrangian action
where [ º denotes Integral ] V8 is an 8-dimensional spacetime, F8 is an Ad28 Spin(8) curvature 2-form, *F is the dual 6-form, S8± is a spinor fermion field, g¶ is the Spin(8) Dirac operator, gg is a gauge-fixing term, and hÝ (dg/dA) ¶h is a ghost term.
The 8-dimensional V8 spacetime of the F4 model is reduced to 4 dimensions by requiring the BRS cohomology 4-form to describe physical spacetime. After dimensional reduction, gravity becomes an effective nonrenormalizable theory, a natural Higgs scalar field appears that gives mass to the weak bosons and Dirac fermions, and there are three generations of fermions. Ratios of volumes of compact manifolds give the following tree-level force strengths, particle masses (constituent masses for quarks), and K-M parameters:
the Kobayashi-Maskawa Parameters are: phase angle e = pi/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