Position variables in classical relativistic hamiltonian mechanics

Abstract

We construct within the equal-time hamiltonian formalism of classical relativistic mechanics, Poincaré invariant and covariant systems of two scalar particles interacting at a distance. Position variables are constructed in terms of the canonical variables of the theory by demanding that they transform under the Lorentz transformations as the space components of four-vectors. The possibility of identifying position variables with canonical coordinates in the center-of-momentum frame is shown. In that particular frame, equations of motion take a simple form and can be solved as in non-relativistic mechanics. A velocity always smaller than that of light is ensured for each particle in the case of a large variety of relativistic potentials which reduce in the non-relativistic limit to the usual central potentials. The present approach is similar to that adopted earlier by Pauri and Prosperi; it differs, however, by the additional requirement of manifest covariance of the underlying theory.