 Massive p-form field

A free massive $p$-form obeys the displayed equation, with the divergence constraint following by applying the codifferential. For $m>0$ and $0\le p\le D-1$, a rest frame leaves an antisymmetric tensor on $D-1$ spatial directions, giving $\left(\genfrac{}{}{0ex}{}{D-1}{p}\right)$ physical polarizations. The mass term removes the ordinary gauge invariance, unless a Stueckelberg mechanism restores a redundant description.

// Target: quantum-field-theory.bigb