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3.5. Weak Force.

SU(2) has 3 infinitesimal generators.

SU(2) acts naturally on each S2 = SU(2)/U(1) of the quaternionic manifold S2xS2, giving the 4-dimensional Lagrangian, with curvature Fw4 and Dirac operator g¶w ,

º (-Fw4/\*Fw4 + `S8± g¶w S8±).

where g¶w acts locally on Q3+ = RP1xS2 = ¶Silov(D3+ Å

Å Spin(5)/SU(2)xU(1)).

V(M) = 2V(S2) and V(Q)/(V(D)^1/m) = V(RP1xS2)/(V(D3+))^1/4.

The resulting volume for the SU(2) weak force is, using volumes from Hua 11:

2V(S2) V(Q3+)/(V(D3+)^1/2 = 2(4¹)(4¹^2)/(¹^3/24)^1/2 =

= 2(25¹^2)(6/¹)1/2 = 2x436.46599 = 872.93198 .

The relative geometric force strength of the SU(2) weak force is the ratio of its volume to the volume of the force with the greatest volume, Spin(5) anti-de Sitter gravitation:

aW = (2V(S2)V(Q3±)/(V(D3±)^1/2) / (V(S4)V(Q5+)/(V(D5+)^1/4) =

= 0.2534577 .

The weak force has a mass factor me^2/(mW+^2 + mW-^2 + mZ^2).

Using particle mass values calculated using the F4 model, the observed weak force constant GW should be given by

GW = aW(me^2/(mW+^2 + mW-^2 + mZ^2)) =

= 0.2534577x(0.511)^2 / ((80.9)^2+(80.9)^2+(92.4)^2) =

= 3.06015 x 10^-12, and GWmproton2 = 1.02 x 10^-5, where the proton mass is calculated from the constituent masses of the up and down quarks to be 938.26 MeV, or 1836.12 times the electron mass.

The SU(2) weak force has a characteristic distance,

the weak force Bohr radius = 1 / aW(mW+ + mW- + mZ) Å 10^-15 cm.

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