On the physical interpretation of the Dirac wavefunction

TL;DR

This paper reinterprets the massless Dirac wavefunction using Geometric Algebra, revealing its connection to electromagnetism and clarifying its symmetry properties and physical interpretation.

Contribution

It introduces a novel geometric algebra framework for the Dirac wavefunction, linking it to classical electromagnetism and clarifying its symmetry and physical properties.

Findings

Recast Dirac spinor as Lorentz scalar, bivector, pseudoscalar fields

Explained 4-pi rotation symmetry as a mathematical artifact

Provided new insights into Dirac bilinears and angular momentum

Abstract

Using the language of the Geometric Algebra, we recast the massless Dirac bispinor as a set of Lorentz scalar, bivector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. The spinor's unusual 4-pi rotation symmetry is seen to be a mathematical artifact of the projection of these fields onto an abstract vector space, and not a physical property of the dynamical fields themselves. We also find a deeper understanding of the spin angular momentum and other Dirac field bilinears in terms of these fields and their corresponding analogues in classical electromagnetism.