  It is shown that in a scale-invariant relativistic field theory, any field
$\psi_n$ belonging to the $(j,0)$ or $(0,j)$ representations of the Lorentz
group and with dimensionality $d=j+1$ is a free field. For other field types
there is no value of the dimensionality that guarantees that the field is free.
Conformal invariance is not used in the proof of these results, but it gives
them a special interest; as already known and as shown here in an appendix, the
only fields in a conformal field theory that can describe massless particles
belong to the $(j,0)$ or $(0,j)$ representations of the Lorentz group and have
dimensionality $d=j+1$. Hence in conformal field theories massless particles
are free.
