Quaternion Dirac Equation and Supersymmetry

TL;DR

This paper analyzes the quaternion Dirac equation, demonstrating its natural incorporation of spin and successful supersymmetrization across various physical scenarios, including mass and electromagnetic potentials.

Contribution

It introduces a consistent supersymmetrization of the quaternion Dirac equation, linking spin structure and electromagnetic interactions.

Findings

Quaternion Dirac equation describes spin components naturally.

Supersymmetrization works for zero and non-zero mass cases.

Splitting in terms of electric and magnetic fields is achieved.

Abstract

Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, non zero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.