Norm Invariance of Mass-Zero Equations under the Conformal Group

It is known that a suitable collection of solutions of the free-field Maxwell's equations is a Hilbert space with respect to an appropriate norm, and that the inhomogeneous Lorentz group acts on this Hilbert space in a unitary and irreducible manner. It is shown that this representation extends to a unitary representation of the conformal group of Minkowski space. Similar results are obtained for other mass-zero relativistic equations.