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We investigate the semiclassical limit from the semi-relativisticHartree-Fock equation describing the time evolution of a system of fermions inthe mean-field regime with a relativistic dispersion law and interactingthrough a singular potential of the form $K(x)=\gamma\frac{1}{|x|^a}$, $a \in\left( \max \left\{ \frac{d}{2} -2 , - 1 \right\}, d-2 \right]$, $d\in\{2,3\}$and $\gamma\in\mathbb{R}$, with the convention $K(x)=\gamma\log(|x|)$ if $a=0$.For mixed states, we show convergence in Schatten norms with explicit ratetowards the Weyl transform of a solution to the relativistic Vlasov equationwith singular potentials, thus generalizing [J. Stat. Phys. 172 (2), 398--433(2018)] where the case of smooth potentials has been treated. Moreover, weprovide new results on the well-posedness theory of the relativistic Vlasovequations with singular interactions.

Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation