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 g¶c,
where g¶c acts locally on Q1,3+ = S5 = ¶Silov(D1,3+ = B6 Å
Å 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 =(8¹^2/3)(4¹^3)/(¹^3/6)^1/4=
= 25¹^4(6¹)^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 Å 10^-13 cm, with energy about 200 MeV.