2012/01/09 by Claudio Cremaschini, Cremaschini, Claudio, Massimo Tessarotto +1
Engineering · Mathematics · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Geophysics and Sensor Technology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems #math-ph #math.MP #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1201.1826
Accepted for publication on EPJ Plus
arxiv created 2012/01/09 · openalex publication_date 2012/01/09 · arxiv updated 2012/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually-interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary and self interactions (EM-interacting N-body systems). In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N-body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary and self EM interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincarè generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie \textquotedblleft no-interaction\textquotedblright theorem for the non-local Hamiltonian system considered here.