Hamiltonian Structure for Classical Electrodynamics of a Point Particle

Details Hamiltonian Structure for Classical Electrodynamics of a Point Particle Hamiltonian Structure for Classical Electrodynamics of a Point Particle

1997-12-08

arxiv.org/abs/physics/9712014v1

Physics

Classical Physics

36 pages, LATEX

Scientific paper

10.1016/S0034-4877(98)80181-X

We prove that, contrary to the common belief, the classical Maxwell electrodynamics of a point-like particle may be formulated as an infinite-dimensional Hamiltonian system. We derive well defined quasi-Hamiltonian which possesses direct physical interpretation being equal to the total energy of the composed (field + particle) system. The phase space of this system is endowed with an interesting symplectic structure. We prove that this structure is strongly non-degenerated and, therefore, enables one to define consistent Poisson bracket for particle's and field degrees of freedom. We stress that this formulation is perfectly gauge-invariant.

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