Relativistic theory of interacting particles

Abstract

The question of whether the ten generators for the Poincaré group as given in a field theoretical model can be reduced to the pure particle space without invalidating the commutation relations is studied. We come to a positive answer in the framework of perturbation theory. In a simple model of scalar particles exchanging scalar bosons we construct the generators in lowest order in the coupling constant and compare the expressions with the ones found by Foldy and Krajcik in a $\frac{1}{c^2}$ expansion. We recover their result, but find in addition new terms in the interaction, which remained principally undetermined in their treatment. Possible useful features of the "relativistically generalized Schrödinger equation" are pointed out.