Poincaré-Invariant Equations of Motion for Classical Particles

Classical particles, and interaction among them governed by second-order equations of motion for the positions of the particles, are considered. Equations of motion, defined for one instant in an arbitrary frame, are derived which are invariant under the Poincar\'e group. The equations of motion are considered invariant if, when the world-line solutions to the equations of motion are transformed, point by point, into a new frame, the new world lines obey the same second-order equation of motion. We illustrate the existence of a wide class of such invariant equations of motion. The further questions of causality and separability are mentioned.