Position Operators in Relativistic Single-Particle Theories

This paper gives formulas for position operators that apply uniformly for all spins of particle. The three-vector X, of the Newton-Wigner and Foldy type, is treated first. Then it is shown that, although X has complicated Lorentz transformation properties, it is linearly related to a certain four-vector $Y_{\mu }$ which is built up from the Poincaré group generators. The four-vector is the generalization of the classical notion of the component of the position four-vector in the direction perpendicular to the world line of the particle.