Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

Details Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

2012-01-09

arxiv.org/abs/1201.1826v1

Physics

Mathematical Physics

Accepted for publication on EPJ Plus

Scientific paper

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 Poincar\`{e} 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.

Affiliated with

Also associated with

No associations

Rating

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643640