Hi, I stumbled upon this dilemma in a homework problem which involved 2D photon gas (unphysical, I know). How many polarization states are there for EM-radiation confined to 2D? In 3D it's 2, but how does it work in 2D? An EM-wave propagating in the z-direction can have its E-component pointing in the x- or y-direction. But obviously that setup is not possible in 2D. Can a photon even propagate in two dimensions, or is this paradox just from the fact that Maxwell's equations (the cross products) don't really work in 2D?