The Dirac algebra and grand unification

TL;DR

This paper explores a novel algebraic framework connecting the Dirac algebra to particle charge structures and broken symmetries, with implications for grand unification and particle mass calculations.

Contribution

It introduces a new representation of the Dirac algebra derived from first principles, linking algebraic structures to particle charges and symmetry breaking in grand unification.

Findings

Relation between Dirac algebra and particle charge combinations

Explicit calculation of running fine structure constants

Suggestions for calculating particle masses

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.