A Lagrangian for quantum electrodynamics is found which makes it explicit
that the photon mass is eventually set to zero in the physical part on
observational ground. It remains possible to obtain a counterterm Lagrangian
where the only non-gauge-invariant term is proportional to the squared
divergence of the potential, while the photon propagator in momentum space
falls off like the inverse squared power of k at large k, which indeed agrees
with perturbative renormalizability. The resulting radiative corrections to the
Coulomb potential in QED are also shown to be gauge-independent. A fundamental
role of the space of four-vectors with components given by four-by-four
matrices is therefore suggested by our scheme, where such matrices can be used
to define a single gauge-fixing function in the functional integral.