A discrete Dirac-K\"{a}hler equation using a geometric discretisation scheme

TL;DR

This paper develops a geometric discretisation scheme for the Dirac-Kähler and Dirac equations, providing a discrete analogue of plane wave solutions to facilitate numerical and theoretical studies.

Contribution

It introduces a novel geometric discretisation approach for the Dirac-Kähler and Hestenes form of the Dirac equation, including discrete plane wave solutions.

Findings

Discrete plane wave solutions established

Geometric discretisation scheme proposed

Potential applications in numerical simulations

Abstract

Discrete models of the Dirac-K\"{a}hler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.