  The relativistic two-body problem is considered for spinless particles
subject to an external macroscopic electromagnetic field. When this field is
made of the monochromatic superposition of two counter-propagating plane waves
(and provided the mutual interaction between particles is known), it is
possible to write down explicitly a pair of coupled wave equations
(corresponding to a pair of mass-shell constraints) which takes into account
also the field contribution. These equations are manifestly covariant;
constants of the motion are exhibited, so one ends up with a reduced problem
involving five degrees of freedom.
