Interacting relativistic particles

Abstract

A manifestly covariant theory of two interacting particles in phase space is presented. Contrary to the implication of the so-called "no-interaction theorem" the coordinates of the particle transform correctly under the Poincaré group. The force law between the particles is quite general. As examples we exhibit explicitly the relativistic generalization of the arbitrary central-force system, such as the simple harmonic oscillator or the Kepler problem. The quantization of these examples is particularly straightforward, and we obtain in closed form the relativistic generalization of their respective spectra. The quantum theory developed is nontrivial, relativistically covariant, and requires neither perturbation theory nor renormalizations.