book chapter published yes Niels P Benedikter author 3DE6C32A-F248-11E8-B48F-1D18A9856A870000-0002-1071-6091 Davide Desio author ea10a57b-23f6-11ef-9085-80d8596d52ef0000-0001-9840-3809 MicheleCorreggi editor MarcoFalconi editor 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 Nature2023 eng 2281-518X 2281-5198 9789819958931 2207.0793910.1007/978-981-99-5894-8_13 57319-333 yes Benedikter NP, Desio D. 2023.Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation. In: Quantum Mathematics I. Springer INdAM Series, vol. 57, 319–333. N. P. Benedikter and D. Desio, “Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation,” in <i>Quantum Mathematics I</i>, 1st ed., vol. 57, M. Correggi and M. Falconi, Eds. Singapore: Springer Nature, 2023, pp. 319–333. 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> Benedikter, Niels P, and Davide Desio. “Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation.” In <i>Quantum Mathematics I</i>, edited by Michele Correggi and Marco Falconi, 1st ed., 57:319–33. SINDAMS. Singapore: Springer Nature, 2023. <a href="https://doi.org/10.1007/978-981-99-5894-8_13">https://doi.org/10.1007/978-981-99-5894-8_13</a>. Benedikter, Niels P., and Davide Desio. “Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation.” <i>Quantum Mathematics I</i>, edited by Michele Correggi and Marco Falconi, 1st ed., vol. 57, Springer Nature, 2023, pp. 319–33, doi:<a href="https://doi.org/10.1007/978-981-99-5894-8_13">10.1007/978-981-99-5894-8_13</a>. N.P. Benedikter, D. Desio, in:, M. Correggi, M. Falconi (Eds.), Quantum Mathematics I, 1st ed., Springer Nature, Singapore, 2023, pp. 319–333. Benedikter, N. P., &#38; Desio, D. (2023). Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation. In M. Correggi &#38; M. Falconi (Eds.), <i>Quantum Mathematics I</i> (1st ed., Vol. 57, pp. 319–333). Singapore: Springer Nature. <a href="https://doi.org/10.1007/978-981-99-5894-8_13">https://doi.org/10.1007/978-981-99-5894-8_13</a> 217392026-04-15T16:38:20Z2026-04-28T10:12:31Z