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We derive the relativistic Vlasov equation from quantum Hartree dynamics forfermions with relativistic dispersion in the mean-field scaling, which isnaturally linked with an effective semiclassic limit. Similar results in thenon-relativistic setting have been recently obtained in [6]. The new challengethat we have to face here, in the relativistic setting, consists in controllingthe difference between the quantum kinetic energy and the relativistictransport term appearing in the Vlasov equation.

From Hartree dynamics to the relativistic Vlasov equation