My Quantum Field Theory notes, after explaining the Lorentz condition, say this: I have some questions about this. 1) What exactly does the polarization of a photon mean? 2) Why do the degrees of freedom of the potentials determine the polarizations of the photon? 3) If instead of the Lorentz condition we used another condition that didn't left any invariance, would it affect the polarizations the photon would have in our theory? Does such a condition even exists, or can it be proved that any condition would leave some residual invariance? Thank you for your time.