If we consider E and B individually, there are 6 total degrees of freedom. But they are actually related to each other by Maxwell's equations. So we can find potentials and reduce dof to 4; 3 in vector potential and 1 in scalar potential. Thus, there remain 2 redundant dof. This is the problem... I think one of them gives the polarization of EM wave and the other gives the gauge symmetry. For example, the vector potential has gauge symmetry, A' = A + del (f) f is scalar and has one dof. Am I understanding right ?