The quantum relativistic two-body problem in time-dependent external potentials

A two-body system with scalar constituents of finite masses is described by a pair of coupled Klein-Gordon equations. The modification required for preserving compatibility in the presence of an external field is nontrivial but can be exactly carried out beyond the static case when the external potential admits a suitable invariance. The conditions ensuring this property are exhibited assuming that the external field is either electromagnetic or a pure spin-two tensor (like a weak gravitational field). Special attention is devoted to apply this method when the field is electromagnetic. Another example is given by an external spin-two field obeying the propagation equation with a mass term. (author) 18 refs