---
OA_place: repository
OA_type: green
_id: '21739'
abstract:
- lang: eng
  text: 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.
alternative_title:
- Springer INdAM Series
article_processing_charge: No
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Davide
  full_name: Desio, Davide
  id: ea10a57b-23f6-11ef-9085-80d8596d52ef
  last_name: Desio
  orcid: 0000-0001-9840-3809
citation:
  ama: '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>'
  apa: '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>'
  chicago: '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>.'
  ieee: '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.'
  ista: '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.'
  mla: 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>.
  short: N.P. Benedikter, D. Desio, in:, M. Correggi, M. Falconi (Eds.), Quantum Mathematics
    I, 1st ed., Springer Nature, Singapore, 2023, pp. 319–333.
date_created: 2026-04-15T16:38:20Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2026-04-28T10:12:31Z
day: '01'
doi: 10.1007/978-981-99-5894-8_13
edition: '1'
editor:
- first_name: Michele
  full_name: Correggi, Michele
  last_name: Correggi
- first_name: Marco
  full_name: Falconi, Marco
  last_name: Falconi
extern: '1'
external_id:
  arxiv:
  - '2207.07939'
intvolume: '        57'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2207.07939
month: '12'
oa: 1
oa_version: Preprint
page: 319-333
place: Singapore
publication: Quantum Mathematics I
publication_identifier:
  eisbn:
  - '9789819958948'
  eissn:
  - 2281-5198
  isbn:
  - '9789819958931'
  issn:
  - 2281-518X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: SINDAMS
status: public
title: Two Comments on the Derivation of the Time-Dependent Hartree–Fock Equation
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
year: '2023'
...