A mechanism for setting the scale for gauge coupling constants

Abstract

The author identifies the spin connection of four-dimensional spacetime with a subgroup of a simple gauge group G. The remaining subgroups of G are the usual internal symmetry groups. Using the work of Weinberg (1983) to relate gauge constants to the circumferences of compact spaces and identifying the known spin of elementary particles with the eigenvalues of the spin connection allows us to set the scale of G. The author can then calculate the remaining gauge coupling constants numerically. The author shows how this mechanism works for the sample calculation where G is SU4, the spin connection is the usual SU2*SU2 and the internal gauge symmetry is U1. The author finds the electromagnetic fine-structure constant to be approximately 1/100.