Two-body relativistic wave equations in external potentials admitting directions of strong translation invariance

Summary

A two-body relativistic system of scalar particles, obeying a pair of coupled Klein-Gordon equations, is embedded into prescribed external potentials. The composition of these interactions can be explicitly carried out for a wide class of potentials, characterized by invariance properties along one or more space-time directions. Various possibilities are unified in a geometric treatment which contains the Bijtebier ansatz as a special case. Compatible equations for the whole system are written down in closed form. Our method is especially appropriate for the degenerate situations where the external field is not static in a unique laboratory frame. More attention is devoted to the case of a uniform constant magnetic field and, for neutral systems, we obtain a covariant law of conservation of the pseudomomentum. This result enables us to eliminate the centre-of-mass variables and the relative time.