A tool kit for staggered fermions

Abstract

We analyze the symmetries of staggered fermions, both discrete and continuous. We present tools that allow a simple decomposition of representations of the continuum symmetries into representations of the discrete lattice symmetries, both at zero and non-zero spatial momenta. We use these tools to find the lattice transcriptions of the operators that appear in the weak interaction hamiltonian. We derive the lattice Ward identities that follow from the single partially conserved axial symmetry. Using these identities we find the lattice equivalents of the continuum PCAC relations. Combining all these tools, we obtain Ward identities for the matrix elements of the weak interaction hamiltonian, from which we derive the behavior of the matrix elements as the pion and kaon masses vanish. We find the same behavior as in the continuum.