  A photon of momentum k can have only two polarization states, not three.
Equivalently, one can say that the magnetic vector potential A must be
divergence free in the Coulomb gauge. These facts are normally taken into
account in QED by introducing two polarization vectors epsilon_\lambda(k) with
lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must
be very discontinuous functions of k and, consequently, their Fourier
transforms have bad decay properties. Since these vectors have no physical
significance there must be a way to eliminate them and their bad decay
properties from the theory. We propose such a way here.
