On euclidean systems of covariance for massless particles

Localizability of a quantum mechanical system is described by a suitable Euclidean system of covariance (ESC). It turns out to be a characteristic feature of relativistic massless particles with non-zero (definite) helicity not to possess localized states for bounded regions. Nevertheless, for physical reasons, a massless particle is expected to be concentratable in bounded regions. We show that ESC, admitting a dilational covariance, describe physical systems which are concentratable in any non-void ball, and give a complete description of these ESC for a massless particle. The description occurs in terms of countable convex combinations of extremal points.