Approximate solutions of predictive relativistic mechanics for short-range scalar interactions

Abstract

We solve the equations of predictive relativistic mechanics for the short-range scalar interaction of two structureless point particles, up to the second order in the coupling constant. The main ideas of this paper are very similar to those of a preceding one dealing with the electromagnetic interaction. But some recent results about the degeneracy of predictive Poincar\'e-invariant systems have also been used to deal with the nontrivial complications which arise from the consideration of short-range interactions.