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

TL;DR

This paper develops a covariant framework for analyzing a neutral two-body quantum system in a constant magnetic field, reducing the problem to a three-dimensional eigenvalue problem and exploring perturbative solutions.

Contribution

It introduces a covariant approach considering motional effects and eigenstates of pseudomomentum, extending the analysis of two-body systems in magnetic fields.

Findings

Reduction to a three-dimensional eigenvalue problem

Inclusion of motional terms in a covariant framework

Perturbative solutions in weak-field and slow-motion regimes

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.