Properties of a New Class of Lattice Dirac Operators

TL;DR

This paper explores a new class of lattice Dirac operators based on a generalized Ginsparg-Wilson relation, analyzing their index theorem and locality properties to advance understanding in lattice gauge theory.

Contribution

It introduces and examines a novel class of lattice Dirac operators defined by a generalized Ginsparg-Wilson relation, expanding theoretical frameworks.

Findings

Analysis of index theorem validity for the new operators

Assessment of locality properties of the operators

Potential implications for lattice gauge theory

Abstract

A new class of lattice Dirac operators $D$ have been recently proposed on the basis of the generalized Ginsparg-Wilson relation, $\gamma_5(\gamma_5 D) + (\gamma_5 D)\gamma_5 =2a^{2k+1}(\gamma_5 D)^{2k+2}$, where $k$ is a non-negative integer. We discuss the index theorem and locality properties for this general class of lattice Dirac operators.