Obtaining the one-body limit from the relativistic two-body equation

We compare several relativistic two-body propagators by writing them in a Lorentz invariant but non-spectral form using relativistic Jacobi coordinates. By doing so we are able, for spin-zero particles, to identify a factor, R, in several of the propagators which is responsible for the incorrect behaviour as one of the particles becomes very heavy (the one-body limit). Since the factor is one for equal-mass particles, it is possible to obtain propagators that agree with the well-known propagators for the equal-mass case but give the correct one-body limit. For Dirac particles the above procedure can still leave positive projection operators which destroy the one-body limit and are inconsistent with Dirac phenomenology. A small additional modification can cure this problem. (orig.)