2005/04/30 by D. Alba, David Alba, L. Lusanna +6 · 4 citations
Engineering · Physics and Astronomy · #Astro and Planetary Science #Astrophysics (astro-ph) #Astrophysics and Star Formation Studies #Atomic and Molecular Clusters (physics.atm-clus) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Sensor Technology #High Energy Physics - Theory (hep-th) #astro-ph #gr-qc #hep-th #physics.atm-clus
paper · pdf · doi:10.48550/arxiv.hep-th/0505005
Latex, p.75, Invited contribution for the book {\it Atomic and Molecular Clusters: New Research} (Nova Science)
arxiv created 2005/04/30 · openalex publication_date 2005/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In non-relativistic mechanics the center of mass of an isolated system is easily separated out from the relative variables. For a N-body system these latter are usually described by a set of Jacobi normal coordinates, based on the clustering of the centers of mass of sub-clusters. The Jacobi variables are then the starting point for separating \it orientational variables, connected with the angular momentum constants of motion, from \it shape (or \it vibrational) variables. Jacobi variables, however, cannot be extended to special relativity. We show by group-theoretical methods that two new sets of relative variables can be defined in terms of a \it clustering of the angular momenta of sub-clusters and directly related to the so-called \it dynamical body frames and \it canonical spin bases. The underlying group-theoretical structure allows a direct extension of such notions from a non-relativistic to a special- relativistic context if one exploits the \it rest-frame instant form of dynamics. The various known definitions of relativistic center of mass are recovered. The separation of suitable relative variables from the so-called \it canonical internal center of mass leads to the correct kinematical framework for the relativistic theory of the orbits for a N-body system with action -at-a-distance interactions. The rest-frame instant form is also shown to be the correct kinematical framework for introducing the Dixon multi-poles for closed and open N-body systems, as well as for continuous systems, exemplified here by the configurations of the Klein-Gordon field that are compatible with the previous notions of center of mass.