Wireframes, Surfaceframes,Volumes, etc.

 Geometric volumesneeded for calculation of forcestrengths 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, whosephoton carries no charge, the factors Vol(Q) and Vol(D) do not applyand are set equal to 1.

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


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