Boundary condition for Staggered Fermion in Lattice Schr\"odinger Functional of QCD

TL;DR

This paper formulates the fermionic part of the Schr"odinger functional in lattice QCD using staggered fermions, analyzing boundary conditions and their implications for numerical calculations of the running coupling.

Contribution

It introduces a boundary condition formulation for staggered fermions in lattice QCD's Schr"odinger functional, considering flavor structure and divergence issues.

Findings

Boundary conditions differ from Symanzik's theory due to species doubling.

Surface divergence is avoided with homogeneous Dirichlet boundary conditions on the original lattice.

Application to numerical calculation of QCD's running coupling is discussed.

Abstract

The fermionic part of the Schr\"odinger functional of QCD is formulated in the lattice regularization with the staggered fermion. The boundary condition imposed on the staggered fermion field are examined in terms of the four-component Dirac spinor. The boundary terms are different from those of the Symanzik's theory in the flavor structure due to the species doubling. It is argued that, in the case of the homogeneous Dirichlet boundary condition, surface divergence does not occur if the link variables of gauge field are introduced on the original lattice, not on the blocked one. Its application to the numerical calculation of the running coupling constant in QCD is discussed.