Staggered Fermion, its Symmetry and Ichimatsu-Patterned Lattice

TL;DR

This paper explores the symmetries of staggered fermions in multiple dimensions, reformulating the Dirac operator with Clifford algebra, clarifying key symmetries, and discussing connections to Ichimatsu-patterned lattices.

Contribution

It introduces a reformulation of the Dirac operator using SO(2D) Clifford algebra and clarifies symmetries in staggered fermions across dimensions, including non-standard modes.

Findings

Clarified chiral, rotational, and parity symmetries in any dimension.

Identified local scalar and pseudo-scalar modes, including non-standard modes.

Discussed the relation to Ichimatsu-patterned lattice approach.

Abstract

We investigate exact symmetries of a staggered fermion in D dimensions. The Dirac operator is reformulated by SO(2D) Clifford algebra. The chiral symmetry, rotational invariance and parity symmetries are clarified in any dimension. Local scalar and pseudo-scalar modes are definitely determined, in which we find non-standard modes. The relation to Ichimatsu-patterned lattice approach is discussed.