Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation Springer INdAM Series Benedikter, Niels P ; https://orcid.org/0000-0002-1071-6091 Desio, Davide ; https://orcid.org/0000-0001-9840-3809 Correggi, Michele Falconi, Marco We revisit the derivation of the time-dependent Hartree–Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comments to the result obtained in 2014 by Benedikter, Porta, and Schlein. First, the derivation holds in arbitrary space dimension. Second, by using an explicit formula for the unitary implementation of particle-hole transformations, we cast the proof in a form similar to the coherent state method of Rodnianski and Schlein for bosons. Springer Nature 2023 info:eu-repo/semantics/bookPart doc-type:bookPart text http://purl.org/coar/resource_type/c_3248 https://research-explorer.ista.ac.at/record/21739 Benedikter NP, Desio D. Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation. In: Correggi M, Falconi M, eds. <i>Quantum Mathematics I</i>. Vol 57. 1st ed. SINDAMS. Singapore: Springer Nature; 2023:319-333. doi:<a href="https://doi.org/10.1007/978-981-99-5894-8_13">10.1007/978-981-99-5894-8_13</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/978-981-99-5894-8_13 info:eu-repo/semantics/altIdentifier/issn/2281-518X info:eu-repo/semantics/altIdentifier/e-issn/2281-5198 info:eu-repo/semantics/altIdentifier/isbn/9789819958931 info:eu-repo/semantics/altIdentifier/e-isbn/9789819958948 info:eu-repo/semantics/altIdentifier/arxiv/2207.07939 info:eu-repo/semantics/openAccess