Stiefel and Grassmann manifolds in quantum chemistry

Autores
Chiumiento, Eduardo Hernan; Melgaard, Michael
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 existence of solutions to Hartree-Fock type equations.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Melgaard, Michael. Dublin Institute of Technology; Irlanda
Materia
Variational Spaces in Hartree-Fock Theory
Banach-Lie Group
Homogeneous Space
Finsler Manifold
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18934
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Stiefel and Grassmann manifolds in quantum chemistryChiumiento, Eduardo HernanMelgaard, MichaelVariational Spaces in Hartree-Fock TheoryBanach-Lie GroupHomogeneous SpaceFinsler Manifoldhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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 existence of solutions to Hartree-Fock type equations.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Melgaard, Michael. Dublin Institute of Technology; IrlandaElsevier Science2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18934Chiumiento, Eduardo Hernan; Melgaard, Michael; Stiefel and Grassmann manifolds in quantum chemistry; Elsevier Science; Journal Of Geometry And Physics; 62; 8; 8-2012; 1866-18810393-0440CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0393044012000927info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2012.04.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:06:21Zoai:ri.conicet.gov.ar:11336/18934instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:06:22.252CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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 Hernan
Variational Spaces in Hartree-Fock Theory
Banach-Lie Group
Homogeneous Space
Finsler Manifold
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 Hernan
Melgaard, Michael
author Chiumiento, Eduardo Hernan
author_facet Chiumiento, Eduardo Hernan
Melgaard, Michael
author_role author
author2 Melgaard, Michael
author2_role author
dc.subject.none.fl_str_mv Variational Spaces in Hartree-Fock Theory
Banach-Lie Group
Homogeneous Space
Finsler Manifold
topic Variational Spaces in Hartree-Fock Theory
Banach-Lie Group
Homogeneous Space
Finsler Manifold
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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 existence of solutions to Hartree-Fock type equations.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Melgaard, Michael. Dublin Institute of Technology; Irlanda
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 existence of solutions to Hartree-Fock type equations.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/18934
Chiumiento, Eduardo Hernan; Melgaard, Michael; Stiefel and Grassmann manifolds in quantum chemistry; Elsevier Science; Journal Of Geometry And Physics; 62; 8; 8-2012; 1866-1881
0393-0440
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18934
identifier_str_mv Chiumiento, Eduardo Hernan; Melgaard, Michael; Stiefel and Grassmann manifolds in quantum chemistry; Elsevier Science; Journal Of Geometry And Physics; 62; 8; 8-2012; 1866-1881
0393-0440
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0393044012000927
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2012.04.005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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