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

Abstract

The internal symmetry of composite relativistic systems is discussed. It is demonstrated that Lorentz-Poincaré 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 2-body system and for an interaction-free many-body system of particles. The issue of localizability of the relativistic CM coordinate is also discussed.

References in corpus (4)

• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• Laplace-Runge-Lenz symmetry in general rotationally symmetric systems
• On the dynamics of classical particle with spin
• Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron