Global-in-time semiclassical regularity for the Hartree-Fock equation

For arbitrarily large times T > 0, we prove the uniform-in-h propagation of semiclassical regularity for the solutions to the Hartree-Fock equation with singular interactions of the form V(x) = +/-|x|(-a) with a is an element of (0, 1/2). As a by-product of this result, we extend to arbitrarily long times the derivation of the Hartree-Fock and the Vlasov equations from the many-body dynamics provided in the work of Chong et al. [arXiv:2103.10946 (2021)]. (C) 2022 Author(s).