D4-D5-E6 Physics -D4=Spin(0,8):

In D4-D5-E6 physics:  

0.  Below the Planck length, or above the Planck energy, 
    the HyperDiamond structure of spacetime breaks down.  
1.  Either discrete or continuous structures can be used
    above Planck length.  Discrete are used at Planck length.
2.  Either compact or noncompact structures can be used.
3.  Antisymmetric representations of the D4 Weyl group give 
    the Lie algebra Spin(0,8) and its Clifford algebra. 
4.  28 generators of Spin(0,8) are gauge bosons.
5.  8-dim vector representation space is spacetime.
6.  8-dim +/-halfspinor row left and right ideals give Dirac operator.
7.  8-dim +halfspinor column left ideal gives fermion spinor particles.
8.  8-dim -halfspinor column right ideal gives antiparticles.
9.  1-dim scalar representation gives Higgs scalar. 
11. classical Lagrangian in 8-dim with first generation fermions 
    is constructed from global E6 symmetry and 
    octonion structure of the Spin(0,8) representations. 
12. Second and third generation fermions 
    come from global E7 and E8 symmetry and produce  
    CP symmetry violation.
13. 8-dim E8 HyperDiamond lattice spacetime splits into 
    an associative 4-dim  HyperDiamond lattice 
    physical spacetime 
    plus 
    a coassociative 4-dim  HyperDiamond lattice 
    internal symmetry space.
14. quantum 4-dim Lagrangian is defined by Many-Worlds 
    sum over Feynman Checkerboard path histories.
15. Dimensional reduction converts Spin(0,8) gauge bosons into 
    gauge bosons for the standard model (with Higgs) plus gravity.
16. Symmetric representations of Weyl groups give 
    Casimir operators, Cohomology, and BRST transformations.
17. quantum theory can be done using BRST transformations.   

The breakdown of the 28 Spin(0,8) gauge bosons

can be seen by looking at reduction of

the Clifford Algebra Cl(0,8) of Spin(0,8) to get

SU(3)xSU(2)xU(1) plus Higgs and Gravity

Click on this Picture to read about the Spin(0,8) Clifford Algebra:

Here is

Quantum Conformal Gravity and Higgs Masses

Kobayshi-Maskawa parameters come from

quark constituent masses and lepton masses.

               d                    s                     b

u            0.975               0.222               -0.00461 i

c           -0.222               0.974                0.0423
            -0.000191 i         -0.0000434 i

t            0.00941            -0.0413               0.999
            -0.00449 i          -0.00102 i

The Kobayashi-Maskawa parameters were calculated from the following

tree-level lepton masses and quark constituent masses:

Me = 0.5110 MeV (assumed);

Me-neutrino = Mmu-neutrino = Mtau-neutrino = 0;

Md = Mu = 312.8 MeV (constituent quark mass);

Mmu = 104.8 MeV;

Ms = 625 MeV (constituent quark mass);

Mc = 2.09 GeV (constituent quark mass);

Mtau = 1.88 GeV;

Mb = 5.63 GeV (constituent quark mass);

Mt = 130 GeV (constituent quark mass).

according to the following formulas:

phase angle e = pi / 2

sin(a) = [Me+3Mu+3Md] /Sqrt( [Me^2+3Mu^2+3Md^2] + [Mmu^2+3Mc^2+3Ms^2] )

sin(b) = [Me+3Mu+3Md] /Sqrt( [Me^2+3Mu^2+3Md^2] + [Mtau^2+3Mt^2+3Mb^2] )

sin(g') = [Mmu+3Mc+3Ms] /Sqrt( [Mmu^2+3Mc^2+3Ms^2] + [Mtau^2+3Mt^2+3Mb^2] )

sin(g) = sin(g') Sqrt( [Mmu+3Mc+3Ms] / [Me+3Mu+3Md] )

As calculated in the model:

Pions and Protons are 4-D versions of: Sine-Gordon Breathers made up of quark-antiquark pairs; and Nontopological Solitons similar to tHooft-Polyakov monopoles made up of rgb quark triples.

In this model, the quark constituent masses are fundamental.

The Planck mass is the mass of a condensate of pions at one point.

Some thoughts about cohomology, quadrics, and dimensional reduction.

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