Two-Body Mass-Shell Constraints in a Constant Magnetic Field (Neutral Case)

Abstract

A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a suitable representation. The relativistic symmetry associated with the magnetic field is carefully respected. Considering eigenstates of the pseudo momentum four-vector, we separate out collective variables and obtain a 3- dimensional reduced equation, posing a nonconventional eigenvalue problem. The velocity of the system as a whole generates "motional" terms in the formulas these terms are taken into account within a manifestly covariant framework.