3-DIMENSIONAL RELATIVISTIC 2-BODY WAVE-EQUATION

It is shown by a simple method that the relativistic two-body wave equation can be written rigorously in a three-dimensional form without making use of the four-dimensional Bethe-Salpeter equation and its reduction. A closed formula for the effective interaction is derived and a perturbation expansion for its evaluation developed in such a way that each order of the approximation not only is relativistic but also takes account of the retardation effect properly, no ambiguity being involved. As an illustration, an explicit expression is given for the ladder approximation.