= Massless induced representation of the Poincare double cover
For a future null standard momentum $k$, choose <Lorentz transformations> $L(p)k=p$ and a <unitary irreducible representation> $d$ of its <little group>. The <Wigner rotation> $R(\Lambda,p)=L(\Lambda p)^{-1}\Lambda L(p)$ acts on the internal state. The resulting <induced representation> acts on wavefunctions with invariant measure $d^3p/(2p^0)$. Trivial little-group translations give fixed <helicity>; nontrivial translations give a <continuous-spin representation> with infinitely many polarization states.
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