Momentum and angular momentum in relativistic classical particle mechanics

Abstract

For a classical-mechanical system of any fixed number of particles it is observed that space-translation invariance and conservation of angular momentum imply conservation of momentum. For three particles it is shown, as previously for two, that Poincaré invariance implies that the total kinematic momentum cannot be a constant of motion unless the accelerations are zero. The equations involved make it appear most likely that this is true for any number of particles.