  We investigate the survival of symmetries in a relativistic system of two
mutually interacting bosons coupled with an external field, when this field is
"strongly" translation invariant in some directions and additionally remains
unchanged by other isometries of spacetime. Since the relativistic interactions
cannot be composed additively, it is not a priori garanteed that the two-body
system inherits all the symmetries of the external potential. However, using an
ansatz which permits to preserve the compatibility of the mass-shell
constraints in the presence of the field, we show how "surviving isometries"
can actually be implemented in the two-body wave equations.
