Remarks on discrete Dirac operators and their continuum limits

TL;DR

This paper examines different definitions of discrete Dirac operators, their continuum limits, and discusses methods like Wilson and staggered fermions to address fermion doubling in lattice field theory.

Contribution

It provides a mathematical analysis of the Wilson and staggered fermion models and their continuum limits, clarifying their properties and differences.

Findings

Analysis of continuum limits of Wilson and staggered fermions

Discussion of mathematical formulations of discrete Dirac operators

Insights into overcoming fermion doubling problem

Abstract

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral subspaces, and it is known as the fermion doubling. In oder to overcome this difficulty, two methods were proposed. The first one is to introduce a new term, called the Wilson term, and the second one is the KS-fermion model or the staggered fermion model. We discuss mathematical formulations of these, and study their continuum limits.