Lattice QED and universality of the axial anomaly

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the l attice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as f or realizations of the Dirac operator that satisfy the Ginsparg-Wilson rela tion. The proof is based on the lattice power counting theorem. The results generalize to non-abelian gauge theories.