Hamiltonian structure for classical electrodynamics of a point particle (Q1290341)

It is proved that the electrodynamics of moving particles may be formulated as an infinite dimensional Hamiltonian system with the particle and field variables kept on the same footing. The corresponding quasi-local Hamiltonian structure is obtained via an appropriate Legendre transformation from the quasi-local Lagrangian defined by \textit{J. Kijowski} and the author [Gen. Relativ. Gravitation 27, No. 3, 267--311 (1995; Zbl 0817.53048)] by using a variational formulation of field theory with respect to accelerated reference frames, related to observer moving along arbitrary space-time trajectories. A nontrivial Poisson bracket structure, consistent with the Poincaré algebra structure of the relativistic theory, is defined by using a strongly nondegenerate symplectic structure defined on the phase space of the composed particle+field system.