Center-of-mass and internal symmetries in classical relativistic systems

The internal symmetry of composite relativistic systems is discussed. It is demonstrated that the Lorentz–Poincare symmetry implies the existence of internal moments associated with the Lorentz boost, which are Laplace–Runge–Lenz (LRL) vectors. The LRL symmetry is thus found to be the internal symmetry universally associated with the global Lorentz transformations, in much the same way as internal spatial rotations are associated with global spatial rotations. Two applications are included for an interacting two-body system and for an interaction-free many-body system of particles. The issue of localizability of the relativistic center-of-mass coordinate is also discussed.