Relativistic Quantum Mechanics of a Neutral Two-Body System in a Constant Magnetic Field

Abstract

A (globally) neutral two-body system is supposed to obey a pair of coupled Klein-Gordon equations in a constant homogeneous magnetic field. Considering eigenstates of the pseudomomentum four-vector, we reduce these equations to a three-dimensional eigenvalue problem. The frame adapted to pseudomomentum has in general a nonvanishing velocity with respect to the frames where the field is purely magnetic. This velocity plays a crucial role in the occurance of motional terms; these terms are taken into account within a manifestly covariant framework. Perturbation theory is available when the mutual interaction doesnot depend on the total energy; a weak-field-slow-motion approximation is more specially tractable.