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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/18934
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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 Técnicas2025-09-29T10:09:12Zoai: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:34982025-09-29 10:09:12.947CONICET 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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1844613968237166592 |
score |
13.070432 |