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Analytical mechanics of a relativistic particle in a positional potential

We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be useful in the study of phenomenological models. Also the Dirac and Klein-Gordon equation differ from the standard formulation, with corrections of order (E-m)/m in the energy spectra.