MMCWMichigan Militia Corps Wolverines
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It was realized by Smith [5] that the presence of the Wyler measure in the expression for [[alpha].sub.EM] given by eq.-(2.1) was consistent with Wheeler ideas that the observed values of the coupling constants of the Electromagnetic, Weak and Strong Force can be obtained if the geometric force strengths (measures related to volumes of complex homogenous domains associated with the U(1), SU(2), SU(3) groups, respectively) are all divided by the geometric force strength of gravity [[alpha].sub.G] (related to the SO(3, 2) MMCW Gauge Theory of Gravity) and which is not the same as the 4D Newton's gravitational constant [G.sub.N] ~ [m.sup.-2.sub.Planck].
in order to evaluate the Wyler measure [[OMEGA].sub.Wyler] [[Q.sub.4]] one requires to embed [D.sub.4] into [D.sub.5] because the Shilov boundary space [Q.sub.4] =[S.sup.3] x R[P.sup.1] is not adequate enough to implement the action of the SO(5) group, the compact version of the Anti de Sitter Group SO(3, 2) that is required in the MacDowell-Mansouri-Chamseddine-West (MMCW) SO(3, 2) gauge formulation of gravity.
This [S.sup.4] [right arrow] E [right arrow] [D.sub.5] bundle is linked to the MMCW SO(3, 2) Gauge Theory formulation of gravity and explains the essential role of the gravitational interaction of the electron in Wyler's formula [5] corroborating Wheeler's ideas that one must normalize the geometric force strengths with respect to gravity in order to obtain the coupling constants.