A Lattice Fermion Doublet With A Generalization Of The Ginsparg-Wilson Relation

TL;DR

This paper introduces a novel staggered discretization of the Dirac operator that yields a fermion doublet with a generalized Ginsparg-Wilson relation, differing from standard staggered fermions in symmetry properties.

Contribution

It proposes a new discretization method for Dirac fermions that produces a physical doublet and generalizes the Ginsparg-Wilson relation, without exact chiral symmetry.

Findings

Produces a fermion doublet interpreted as a physical particle pair.

No exact chiral symmetry is present, but a generalized Ginsparg-Wilson relation is satisfied.

Differentiates real and imaginary parts across different nodes in the lattice.

Abstract

We present a new staggered discretization of the Dirac operator. In comparison with standard staggered fermions, real and imaginary parts are located in different nodes. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. Contrary to usual staggered fermions, we have no exact chiral symmetry but obtain a generalization of the Ginsparg-Wilson relation.