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3.3. Color Force.

 SU(3) has 8 infinitesimal generators, giving the color force. SU(3) acts naturally on the quaternionic manifold CP2 = SU(3)/S(U(2) x U(1)), giving the 4-dimensional Lagrangian, with curvature Fc4 and Dirac operator gc,

( - Fc4/\*Fc4 + `S8± gc S8± )

where gc acts locally on Q1,3+ = S5 = Silov(D1,3+ = B6

SU(4)/S(U(3) x U(1)).

V(M) = V(CP2) and V(Q)/(V(D)^1/m) = V(S5)/(V(B6))^1/4.

The resulting volume for the SU(3) color force is, using volumes from Hua 11:

V(CP2) V(Q1,3+)/(V(D1,3+))^1/4 =(8^2/3)(4^3)/(^3/6)^1/4=

 = 25^4(6)^1/4 / 3 = 2164.978 .

The relative geometric force strength of the SU(3) color force is the ratio of its volume to the volume of the force with the greatest volume, Spin(5) anti-de Sitter gravitation:

aC = (V(CP2)V(Q1,3+)/(V(D1,3+)^1/4)/(V(S4)V(Q5+)/(V(D5+)^1/4) =

   = 0.6286062 .

The SU(3) color force has no mass factor.

The characteristic distance of the SU(3) color force is about the size of a proton, the color force bohr radius 1/aCmd 10^-13 cm, with energy about 200 MeV.

 

 


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