The construction of generalized Dirac operators on the lattice

TL;DR

This paper presents a systematic method for constructing generalized Dirac operators on the lattice that incorporate various structures while respecting key symmetries, aiding future research in lattice gauge theories.

Contribution

It introduces a comprehensive framework for building Dirac operators with arbitrary features and symmetry properties on the lattice, expanding the toolkit for lattice gauge theory studies.

Findings

Provides explicit examples of generalized Dirac operators.

Demonstrates how to preserve symmetries in lattice constructions.

Offers guidance for extending the set of Dirac operators.

Abstract

We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic rotations and reflections) on the lattice. We give an extensive set of examples and offer help to add further structures.