= Massive Pauli-Lubanski Casimir
{title2=$W^2=-m^2s(s+1)$}
For a massive positive-energy <unitary irreducible representation> of the <Poincaré group> with signature $(+---)$, choose a rest frame. The <Pauli-Lubanski pseudovector> has zero time component and spatial components $mJ_i$, up to a common sign convention. Its square is therefore $-m^2\mathbf J^2$. The <SU(2)> little-group representation has <spin> $s$ and $\mathbf J^2=s(s+1)$, proving the invariant value. The mass and spin label the <massive induced representation of the Poincare double cover>.
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