Wigner translations and the observer-dependence of the position of masslesss spinning particles

Abstract

The Wigner little group for massless particles is isomorphic to the Euclidean group ${\rm SE}(2)$. Applied to momentum eigenstates, or to infinite plane waves, the Euclidean "Wigner translations" act as the identity. We show that when applied to finite wavepackets the translation generators move the packet trajectory parallel to itself through a distance proportional to the particle's helicity. We relate this effect to the Hall effect of light and to the Lorentz-frame dependence of the position of a massless spinning particle.