Chiral Dirac Fermions on the Lattice using Geometric Discretisation

TL;DR

This paper introduces a geometric discretisation scheme for chiral Dirac fermions on the lattice, effectively avoiding species doubling and accurately capturing chirality through the Dirac-Kahler formalism.

Contribution

It presents a novel discretisation approach based on Dirac-Kahler formalism that preserves algebraic relations and prevents species doubling in lattice fermions.

Findings

Avoids traditional species doubling in lattice fermions

Successfully captures chirality using geometric discretisation

Provides a consistent algebraic framework for lattice Dirac operators

Abstract

We propose a discretisation scheme based on the Dirac-Kahler formalism (DK) in which the algebraic relations between continuum operators ${\wedge, d, \star}$ are captured by their discrete analogues, allowing the construction of the relevant projection operators necessary to prevent species doubling. We thus avoid the traditional form of species doubling as well as spectral doubling, which does not occur in the DK setting. Chirality is also captured, since we have $\star$ from geometric discretisation.