# Real spinors and real Dirac equation

## TL;DR

This paper revisits the geometric algebra formulation of the Dirac equation, revealing a natural extension to non-Abelian gauge potentials through the minimal coupling procedure.

## Contribution

It introduces a non-Abelian generalization of electromagnetic gauge potential within the real Clifford algebra framework of the Dirac equation.

## Key findings

- Reexamination of minimal coupling in geometric algebra
- Identification of spinors with even elements of real Clifford algebra
- Proposal of a non-Abelian gauge extension

## Abstract

We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of spacetime. This point of view, as we argue, leads naturally to a non-Abelian generalisation of the electromagnetic gauge potential.