Discrete Dirac-K\"ahler equation and its formulation in algebraic form

TL;DR

This paper explores the connection between the discrete Dirac-Kähler equation and discrete Dirac-type equations within geometric spacetime algebra, showing how solutions relate through sum and difference operations.

Contribution

It introduces a novel algebraic formulation linking the discrete Dirac-Kähler equation to discrete Dirac equations, enhancing understanding of their interrelation.

Findings

Solutions of the Dirac-Kähler equation can be expressed as sums and differences of solutions to discrete Dirac equations.

The paper establishes a clear algebraic relationship between these discrete equations.

It provides a framework for representing solutions in algebraic form.

Abstract

A relationship between the discrete Dirac-K\"ahler equation and discrete analogues of some Dirac type equations in the geometric spacetime algebra is discussed. We show that a solution of the discrete Dirac-K\"ahler equation can be represented as the sum and difference of solutions of discrete Dirac type equations with the corresponding sign of the mass term.