Relativistic corrections in a three-boson system of equal masses
Résumé
Three-body systems of scalar bosons are covariantly described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the mass-shell constraints can be reduced to a three-dimensional eigenvalue problem. In general, the reduced equation obtained by this procedure involves the spectral parameter in a nonconventional manner, but for three equal masses a drastic simplification arises at the first post-Galilean order: the reduced wave equation becomes a conventional eigenvalue problem that we treat perturbatively, computing a first-order correction beyond the nonrelativistic limit. The harmonic interaction is displayed as a toy model.