Gauge fixing and gauge correlations in noncompact Abelian gauge models

We investigate some general properties of linear gauge fixings and gauge-field correlators in lattice models with noncompact U(1) gauge symmetry. In particular, we show that, even in the presence of a gauge fixing, some gauge-field observables (like the photon-mass operator) are not well-defined, depending on the specific gauge fixing adopted and on its implementation. Numerical tests carried out in the three-dimensional noncompact lattice Abelian Higgs model fully support the analytical results and provide further insights.