Center-of-mass motion of a system of relativistic Dirac particles

The relativistic center-of-mass motion for a system ofN fermions can be exactly separated because of the linearity of the Dirac operators in momenta which is not possible for quadratic Klein-Gordon particles. The covariant equations derived from Maxwell-Dirac field theory are considered. The center-of-mass equation is still a 4^N-component spinor equation. We solve these equations for two- and three-body systems, as well as the relative motion for the non-interacting case, and discuss the quantum numbers and identification of eigenstates and eigenvalues. The results apply for both bound and scattering states.Dedicated to the Third Centenary of the Publication of Principia: Corollary IV.... and therefore the common center of gravity of all bodies acting upon each other (excluding external actions and impediments) is either at rest, or moves uniformly in a right line. Is. Newton, Philosophiae Naturalis Principia Mathematica (S. Pepys, Julii 5, 1686, Londini)