Chiral Dirac fermions on the lattice using Geometric Discretisation

TL;DR

This paper introduces a novel geometric discretisation method for implementing chiral Dirac fermions on a lattice, addressing the fermion doubling problem using Dirac-Kahler theory.

Contribution

It presents a new discretisation approach based on geometric principles that effectively extracts Dirac fields in lattice gauge theories.

Findings

Addresses fermion doubling problem

Provides a new discretisation framework

Demonstrates effective Dirac field extraction

Abstract

A new approach to the problem of doubling is presented with the Dirac-Kahler (DK) theory as a starting point and using Geometric Discretisation providing us with a new way of extracting the Dirac field in the discrete setting of a hyper-cubic complex.