A nonlocal discretization of fields

TL;DR

This paper introduces a nonlocal discretization method for classical fields that avoids common lattice theory issues like fermion doubling and chiral symmetry breaking by using matrix derivatives on a non-equispaced lattice.

Contribution

The paper presents a novel nonlocal discretization approach that constructs derivatives via matrix representations on non-equispaced lattices, eliminating typical lattice theory drawbacks.

Findings

Eliminates fermion doubling problem.

Preserves chiral symmetry in massless case.

Uses well-behaved matrix derivatives on non-equispaced lattices.

Abstract

A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion doubling or the breaking of chiral symmetry for the massless case, are absent in this method.