Colored Quaternion Dirac Particles of Charges 2/3 and -1/3

TL;DR

This paper extends Dirac's equation by using quaternion coefficients to derive quasi-particles with fractional charges of 2/3 and -1/3, linking color charge and Q covariance with minimal assumptions.

Contribution

It introduces a quaternion-based formulation of Dirac's equation that naturally yields fractional charge particles and explores the implications of Q covariance for color neutrality.

Findings

Derivation of fractional charge quasi-particles from quaternion Dirac equation

Connection between quaternion imaginary bases and color charge

Necessity of color neutrality due to Q covariance

Abstract

By starting with the simpliest expression of the first order linear wave equation (Dirac's equation) and by confining the elements of the coefficients (matrices) to the quaternions, it is shown that the association of the imaginary bases of the quaternions with three "colors" and their conserved currents results in quasi-particles with charges of 2/3 and -1/3 with a minimum of assumptions. It is shown how color neutral particles are required by Q covariance, first discussed by Finkelstein, et. al. in 1963.