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3.2. Electromagnetism.

 The electromagnetic photon has 4 covariant components, each of which may be taken to act on a 1-dimensional S1 subspace of

T4 = S1 x S1 x S1 x S1, each U(1) corresponding to the x, y, z, and t covariant components of the U(1) photon, giving the 4-dimensional Lagrangian, with curvature Fem4 and Dirac operator ge,

( - Fem4/\*Fem4 + `S8± ge S8± ) .

V(M) = 4V(S1) and V(Q)/(V(D)1/m) = 1, so the resulting volume for U(1) electromagnetism is

4V(S1) &endash; 1 = 4(2) = 8 = 4 x 6.2831853 = 25.132741 .

The relative geometric force strength of U(1) electromagnetism is the ratio of its volume to the volume of the force with the greatest geometric volume, Spin(5) anti-de Sitter gravitation, for which the calculation is made independently in Section 3.4.:

aE = (4V(S1))/(V(S4)V(Q5+)/(V(D5+)^1/4) = 1/137.03608 .

U(1) electromagnetism has no mass factor.

The characteristic distance of U(1) electromagnetism is about the size of an atom, the electromagnetic bohr radius 1/aEme 5 x 10^-9 cm, with energy about 4 Kev.

 

 


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