Stiefel and Grassmann manifolds in quantum chemistry

Autores
Chiumiento, Eduardo Hernán; Melgaard, M.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove that they are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on the existence of solutions to Hartree-Fock type equations.
Facultad de Ciencias Exactas
Materia
Matemática
Banach-Lie group
Finsler manifold
Homogeneous space
Variational spaces in Hartree-Fock theory
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/84703
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/84703
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Stiefel and Grassmann manifolds in quantum chemistryChiumiento, Eduardo HernánMelgaard, M.MatemáticaBanach-Lie groupFinsler manifoldHomogeneous spaceVariational spaces in Hartree-Fock theoryWe establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove that they are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on the existence of solutions to Hartree-Fock type equations.Facultad de Ciencias Exactas2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1866-1881http://sedici.unlp.edu.ar/handle/10915/84703enginfo:eu-repo/semantics/altIdentifier/issn/0393-0440info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2012.04.005info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T16:56:52Zoai:sedici.unlp.edu.ar:10915/84703Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 16:56:53.101SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Stiefel and Grassmann manifolds in quantum chemistry
title Stiefel and Grassmann manifolds in quantum chemistry
spellingShingle Stiefel and Grassmann manifolds in quantum chemistry
Chiumiento, Eduardo Hernán
Matemática
Banach-Lie group
Finsler manifold
Homogeneous space
Variational spaces in Hartree-Fock theory
title_short Stiefel and Grassmann manifolds in quantum chemistry
title_full Stiefel and Grassmann manifolds in quantum chemistry
title_fullStr Stiefel and Grassmann manifolds in quantum chemistry
title_full_unstemmed Stiefel and Grassmann manifolds in quantum chemistry
title_sort Stiefel and Grassmann manifolds in quantum chemistry
dc.creator.none.fl_str_mv Chiumiento, Eduardo Hernán
Melgaard, M.
author Chiumiento, Eduardo Hernán
author_facet Chiumiento, Eduardo Hernán
Melgaard, M.
author_role author
author2 Melgaard, M.
author2_role author
dc.subject.none.fl_str_mv Matemática
Banach-Lie group
Finsler manifold
Homogeneous space
Variational spaces in Hartree-Fock theory
topic Matemática
Banach-Lie group
Finsler manifold
Homogeneous space
Variational spaces in Hartree-Fock theory
dc.description.none.fl_txt_mv We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove that they are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on the existence of solutions to Hartree-Fock type equations.
Facultad de Ciencias Exactas
description We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove that they are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on the existence of solutions to Hartree-Fock type equations.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/84703
url http://sedici.unlp.edu.ar/handle/10915/84703
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0393-0440
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2012.04.005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1866-1881
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 12.723966

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