Localizability, gauge symmetry and Newton-Wigner operator for massless particles

TL;DR

This paper explores the concept of position operators for massless spinning particles, linking coordinate noncommutativity to gauge symmetry and analyzing the limitations of the Newton-Wigner operator for different helicities.

Contribution

It provides a detailed discussion on the position operator for massless particles, highlighting gauge symmetry implications and the helicity-dependent applicability of the Newton-Wigner operator.

Findings

Coordinate noncommutativity relates to gauge symmetry.

Newton-Wigner operator applies only for helicity |λ| ≤ 1/2.

Analysis clarifies limitations of position operators for massless particles.

Abstract

The notion of position operator for massless spinning particles is discussed in some detail. The noncommutativity of coordinates is related to the gauge symmetry following from the freedom in definition of standard state in Wigner's construction of induced representations of Poincare group. The counterpart of Newton-Wigner operator is discussed. It is explained why the Newton-Wigner construction works only for helicity $ \mid\lambda\mid\leq1/2$.