Characters of Lattice Fermions Based on the Hyperdiamond Lattice

TL;DR

This paper explores minimal-doubling fermion actions on hyperdiamond lattices, proposing improved constructions and conditions for Lorentz covariance, highlighting the importance of non-nearest-site hoppings, and introducing new classes of actions.

Contribution

It introduces an improved spatial construction of Creutz fermion actions on deformed hyperdiamond lattices and proposes new classes of minimal-doubling actions on hypercubic lattices.

Findings

Non-nearest-site hoppings are essential for correct excitations.

Proposed a class of minimal-doubling actions on deformed hypercubic lattices.

Introduced a two-parameter class of Wilczek-type minimal-doubling actions.

Abstract

We study minimal-doubling fermion actions on hyperdiamond and deformed hyperdiamond lattices, with emphasis on the real-space construction of them and Lorentz covariance of excitations from fermion poles. We propose the improved spatial construction of Creutz fermion action on a deformed hyperdiamond lattice, and discuss conditions for a hyperdiamond-lattice action to produce Lorentz-covariant excitations from poles of fermion propagators. It is pointed out that the non-nearest-site hoppings are essential for the correct excitations. We propose a class of minimal-doubling actions defined on a deformed hypercubic lattice as a generalization of Creutz-type actions. In addition we introduce a two-parameter class of Wilczek-type minimal-doubling actions.