 Massless p-form gauge field

A massless Abelian $p$-form in $D$-dimensional flat spacetime transforms on shell as an antisymmetric rank-$p$ tensor of the rotational little group $SO(D-2)$. Its physical state count is $\left(\genfrac{}{}{0ex}{}{D-2}{p}\right)$. A compatible real self-duality constraint halves this count. A four-dimensional three-form has no local propagating polarization.