Localization of Massless Spinning Particles and the Berry Phase

TL;DR

This paper investigates the position operator for massless spinning particles like photons, revealing anomalous commutation relations linked to Berry phase effects, supported by experimental evidence from the Tomita-Chiao experiment.

Contribution

It introduces a relativistic quantum framework with non-commuting position operators for massless spinning particles, connecting Berry phase to photon localization.

Findings

Position operators have anomalous commutators proportional to helicity.

Ray representations of translations arise from non-commuting position components.

Experimental support from the Tomita-Chiao experiment confirms the theory.

Abstract

The components of the position operator, at a fixed time, for a massless and spinning particle with given helicity $\lambda$ described in terms of bosonic degrees of freedom have an anomalous commutator proportional to $\lambda$. The position operator generates translations in momentum space. We show that a ray-representation for these translations emerges due to the non-commuting components of the position operators and relate this to the Berry-phase for photons. The Tomita-Chiao experiment then gives support for this relativistic and quantum mechanical description of photons in terms of non-commuting position operators.