Renormalization counterterms in linearized lattice QED

We analyze in weak-coupling perturbation theory the renormalization-counterterm structure of linearized lattice quantum electrodynamics (QED). We find that, although the linearized theory is gauge invariant, counterterms appear that would be forbidden by the Ward identities in the compact formulation of lattice QED. For example, the photon develops a mass, the light-by-light scattering amplitude becomes noncovariant, and the coupling constant is renormalized even in the quenched version of the theory. Gauge invariance does not preclude the appearance of such counterterms in the linearized theory because the formulation is nonlocal