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.

arXiv comment13 pages, 3 figures. PDFTeX

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• Geometrodynamics of Spinning Light
• Chiral Kinetic Theory
• Lorentz Invariance in Chiral Kinetic Theory
• Topological spin transport of photons: the optical Magnus Effect and Berry Phase
• Spin Hall effect and Berry phase of spinning particles
• Fermat Principle for spinning light
• Relativistic Hall Effect
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• Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
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• Wigner-Souriau translations and Lorentz symmetry of chiral fermions
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• Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion
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• Consistent Relativistic Chiral Kinetic Theory: a derivation from OSEFT
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• Chiral Wave-packet Scattering in Weyl Semimetals
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• Position, spin and orbital angular momentum of a relativistic electron
• The chiral vortical effect in Wigner function approach
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• Helicity of spin-extended chiral particles
• Probing Wigner Rotations for Any Group
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• The covariance of chiral fermions theory
• Berry Phase Physics in Free and Interacting Fermionic Systems
• Collective dynamics of Fermi-surface fluctuations in an interacting Weyl metal phase
• Spin Hall effects and the localization of massless spinning particles