The Dirac algebra and grand unification
Abstract
A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and quaternions which can be applied to the broken symmetry between the three nongravitational interactions. The significance of this relation for Grand Unification is derived by explicit calculation of the running values of the fine structure constants, with suggestions for the calculation of particle masses.
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