Lattice fermions: Species doubling, chiral invariance and the triangle anomaly

Abstract

We investigate the formulation of fermions in lattice gauge theories, in weak coupling perturbation theory. It is shown that a lattice fermion formulation without species doubling and with explicit continuous chiral symmetry is impossible. We interpret this as a manifestation of the triangle anomaly. Green functions and (axial) vector flavor currents in lattice QCD with Wilson fermions are studied. We show that in the (weak coupling) continuum limit the theory is equivalent to perturbative continuum QCD: chiral invariant and with the usual anomaly in the flavor singlet axial current.