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 $\mathrm{SE}(2)$. 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.

13 pages, 3 figures. PDFTeX

References in corpus (5)

• Geometrodynamics of Spinning Light
• Lorentz Invariance in Chiral Kinetic Theory
• Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
• Chiral fermions as classical massless spinning particles
• Wigner-Souriau translations and Lorentz symmetry of chiral fermions

Cited by in corpus (15)

• Collisions in Chiral Kinetic Theory
• Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics
• Gravitational spin Hall effect of light
• Foundations and Applications of Quantum Kinetic Theory
• Propagation of polarized gravitational waves
• Zilch Vortical Effect, Berry Phase, and Kinetic Theory
• Wigner-Souriau translations and Lorentz symmetry of chiral fermions
• Position, spin and orbital angular momentum of a relativistic electron
• Frequency- and polarization-dependent lensing of gravitational waves in strong gravitational fields
• Spin Hall effects in the sky
• Lorentz transformations, sideways shift and massless spinning particles
• Weyl geometric effects on the propagation of light in gravitational fields
• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• Conformal symmetry, chiral fermions and semiclassical approximation
• Spin Hall effects and the localization of massless spinning particles