Genuine Symmetry of a Staggered Fermion

Abstract

We present a new formulation of a staggered fermion on a D-dimensional lattice based on the SO(2D) Clifford algebra, which is naturally contained in the action. The action of a massless staggered fermion is invariant under discrete rotations and SO(2D) chiral and other discrete transformations. From the transformation properties of the fermion, we find two local meson operators (one scalar and one pseudoscalar), in addition to two standard meson operators. * )

Rotational Symmetry and a Light Mode in Two-Dimensional Staggered Fermions

“…To split the masses of degenerate tastes, we introduce four rotationally invariant operators, which we denote 14) for the original staggered fermion action (2 . 4).…”

“…13) For the control of their operators which preserve the discrete rotational symmetry, we make use of staggered fermions on a D-dimensional lattice space based on the SO(2D) Clifford algebra. 14) In the ordinary staggered fermion formulation, the representation of the rotational symmetry can be realized only after the continuum limit is taken. Actually, the spinor representation is closely related to the sign factor η µ (n), and it is a nontrivial problem to realize the eigenmodes of the Dirac operator as spinors.…”

“…Our approach is based on that of Ref. 14), in which there is a discrete rotational invariance of the staggered fermion action and an explicit rotational representation. If we require this invariance and representation for staggered fermions even in the case of a finite lattice constant, a strong constraint is imposed on our improved action.…”

“…Only these four operators preserve the discrete rotational symmetry in any number of dimensions. 14) The total mass matrix analysis is insufficient, because the matrix does not commute with the kinetic term. Therefore, we also analyze the propagator and the pole.…”

“…14) The basic idea of this formulation is that the number of dimensions of the total representation space, including the spinor and taste spaces, 2 D , is the same as that of an SO(2D) spinor representation. The quantity 2 D is the same as the number of sites in a D-dimensional hypercube.…”