Chiral properties of discrete Joyce and Hestenes equations

TL;DR

This paper investigates how chirality is represented in discrete versions of the Dirac-Kähler equation, introducing projectors, spin operators, and demonstrating chiral symmetry in the discrete models.

Contribution

It presents a novel discrete framework for Dirac-Kähler equations that captures chirality and spin properties, extending the understanding of discrete quantum models.

Findings

Discrete chiral states are described using projectors.

The model admits a chiral symmetry.

Discrete spin operators and eigenstates are constructed.

Abstract

This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-K\"{a}hler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be described with the aid of some projectors on a space of discrete forms. The proposed discrete model admits a chiral symmetry. We construct discrete analogues of spin operators, describe spin eigenstates for a discrete Joyce equation, and also discuss chirality.