Discrete Dirac-K\"ahler and Hestenes equations

TL;DR

This paper develops a discrete version of the Dirac equation in Hestenes form using Clifford algebra on discrete forms, exploring its relation to the Dirac-Kähler equation.

Contribution

It introduces a novel discrete analogue of the Dirac-Hestenes equation by defining Clifford products on discrete forms, linking it to the Dirac-Kähler framework.

Findings

Constructed a discrete Dirac-Hestenes equation using Clifford algebra.

Established the relation between discrete Dirac-Kähler and Hestenes equations.

Abstract

A discrete analogue of the Dirac equation in the Hestenes form is constructed by introduction the Clifford product on the space of discrete forms. We discuss the relation between the discrete Dirac-K\"{a}hler equation and a discrete Hestenes equation.