On the Physical Interpretation of the Dirac Wavefunction II: The Massive Dirac Field

TL;DR

This paper reformulates the massive Dirac equation using Geometric Algebra, interpreting the wavefunction as a set of classical fields obeying Maxwell-like equations, and clarifies the role of the imaginary unit in this context.

Contribution

It introduces a field-based geometric interpretation of the Dirac wavefunction, providing new insights into discrete symmetries and the structure of the Dirac algebra.

Findings

Recast Dirac bispinor as Lorentz scalar, vector, bivector, pseudovector, and pseudoscalar fields.

Derived a generalized Maxwell-like set of equations for these fields.

Clarified the distinction between geometric and non-geometric imaginary units in the algebra.

Abstract

Using the language of the Geometric Algebra, we recast the massive Dirac bispinor as a set of Lorentz scalar, vector, bivector, pseudovector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. This field-based formulation requires careful distinction between geometric and non-geometric implementations of the imaginary unit scalar in the Dirac algebra. This distinction, which is obscured in conventional treatments, allows us to find alternative constructions of the field bilinears and a more natural interpretation of the discrete C, P, and T transformations.