= Stueckelberg mechanism
{c}
{title2=$A_p-m^{-1}dC_{p-1}$}
For $p\ge1$, introduce a $(p-1)$-form $C$ and replace the mass term of a <massive p-form field> by one built from $A-m^{-1}dC$. The transformations $A\mapsto A+d\Lambda$, $C\mapsto C+m\Lambda$ leave this combination and $dA$ invariant. Gauge fixing $C=0$ recovers the original massive theory. Its massless-component counts add as $\binom{D-2}{p}+\binom{D-2}{p-1}=\binom{D-1}{p}$, explaining the longitudinal degrees of freedom and the corresponding assembly of nonzero <Kaluza-Klein modes>.
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