Wireframes, Surfaceframes, Volumes, etc.

 Geometric volumes needed for calculation of force strengths include:

Force       M      Vol(M)
gravity    S^4    8pi^2/3 - S^4 is 4-dimensional 

color      CP^2   8pi^2/3 - CP^2 is 4-dimensional

weak   S^2 x S^2  2 x 4pi - S^2 is a 2-dim boundary of 3-dim ball
                            4-dim S^2 x S^2 =
                            = topological boundary of 6-dim 2-polyball 
                     Shilov Boundary of 6-dim 2-polyball = S^2 + S^2 = 
                            = 2-dim surface frame of 4-dim S^2 x S^

e-mag      T^4    4 x 2pi - S^1 is 1-dim boundary of 2-dim disk 
                            4-dim T^4 = S^1 x S^1 x S^1 x S^1 =
                            = topological boundary of 8-dim 4-polydisk
                     Shilov Boundary of 8-dim 4-polydisk = 
                            = S^1 + S^1 + S^1 + S^1 = 
                            = 1-dim wire frame of 4-dim T^4

Also note that:

For U(1) electromagnetism, whose photon carries no charge, the factors Vol(Q) and Vol(D) do not apply and are set equal to 1.

From another point of view, the link manifold to the target vertex is trivial for the abelian neutral U(1) photons of Electromagnetism, so we take QE and DE to be equal to unity.

Tony's Home Page ------------------------ Here is a pdf version of this Wireframes ... etc. page.