Note on rotational properties of position operators of massless particles

Abstract

Nonlinear action of the group of spatial rotations on commuting components of a position operator of a massless particle of arbitrary helicity is studied. It is shown that linearization of this action necessarily leads to the Pryce operator with non-commuting components. The problem is also analyzed from a geometric perspective using Callan, Coleman, Wess and Zumino method.

15 pages, improved version

References in corpus (3)

• The geometrical interpretation of the photon position operator
• Construction of a photon position operator with commuting components from natural axioms
• The explicit form of the unitary representation of the Poincaré group for vector-valued wave functions (massive and massless), with applications to photon's localization and position operators