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

TL;DR

This paper investigates how Wigner translations affect finite wavepackets of massless spinning particles, revealing a helicity-dependent shift in their position that relates to the observer-dependence of their localization.

Contribution

It demonstrates that Wigner translations cause a helicity-dependent displacement of finite wavepackets, linking Lorentz-frame dependence and optical Hall effects.

Findings

Wigner translations shift finite wavepackets proportionally to helicity

The effect explains observer-dependent position of massless particles

Connects Lorentz transformations with optical Hall phenomena

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.