Relative Position Representation for a Relativistic Two-Particle System

Abstract

Two-particle angular momentum states are constructed which are localized with respect to the magnitude of the relative position in the rest system and which have arbitrary 3-momentum dependence. The associated relative position operator is constructed, and a quantum-mechanical analog of the classical impact parameter is identified. Two-particle angular momentum states are constructed, which are also localized with respect to the ``mean-position'' of the 2-particle system, and the associated ``mean-position'' operator is seen to be a generalization of the 1-particle Newton-Wigner position operator.