Quaternionic Electron Theory: Geometry, Algebra and Dirac's Spinors

TL;DR

This paper explores the use of complexified quaternions and $i$-complex geometry to provide new geometric interpretations of the Dirac equation, enhancing understanding of electron spinor representations.

Contribution

It introduces a quaternionic framework for the Dirac equation, offering novel geometric insights not apparent in traditional matrix-based methods.

Findings

Quaternionic formulation offers clearer geometric interpretation of spinors

Provides alternative algebraic approach to Dirac equation

Enhances conceptual understanding of electron spin and geometry

Abstract

The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.