Symmetries of the Relativistic Two-Boson System in External Field
Résumé
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 the ``surviving isometries'' can actually be implemented in the two-body wave equations.