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Hamiltonian and the space-time structure
@Shaktyai Hi, in my answer below I have followed another approach. The relativistic dynamics of a charged particle is Hamiltonian w.r.t. the free particle Hamiltonian $H$ and the symplectic form $\omega_0+\omega_F,$ where $\omega_0$ is the canonical symplectic form on the phase space while $\omega_F$ comes from the Faraday tensor.