Aliasing modes in the lattice Schwinger model

TL;DR

This paper investigates how aliasing effects on a specialized lattice for the Schwinger model influence the emergence of new modes and alter the boson mass in the continuum limit.

Contribution

It introduces a lattice based on Hermite polynomial zeros that reveals aliasing modes and modifies the Klein-Gordon equation and mass in the continuum limit.

Findings

Aliasing modes appear due to boundary effects on the lattice.

The lattice reproduces the Klein-Gordon equation with the correct mass asymptotically.

Boundary considerations lead to new modes and a reduced mass in the continuum limit.

Abstract

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass.