A promenade through singular symplectic geometry

https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.ca

Detalhes bibliográficos
Autor: Nicolás Martínez, Pablo
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/433042
Acesso em linha:https://hdl.handle.net/2117/433042
https://dx.doi.org/10.2436/20.2002.02.43
Access Level:acceso abierto
Palavra-chave:Poisson geometry
Reduction
Minimal coupling
Lie algebroid
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::53 Differential geometry::53C Global differential geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística
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oai_identifier_str oai:upcommons.upc.edu:2117/433042
network_acronym_str ES
network_name_str España
repository_id_str
spelling A promenade through singular symplectic geometryNicolás Martínez, PabloPoisson geometryReductionMinimal couplingLie algebroidClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometryClassificació AMS::53 Differential geometry::53C Global differential geometryÀrees temàtiques de la UPC::Matemàtiques i estadísticahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.caIn this article, we present symplectic and Poisson geometry from the perspective ofHamiltonian mechanics. We then introduce symplectic Lie algebroids, objects whichlie between symplectic and Poisson manifolds. Afterwards, we recall the notion ofsymplectic reduction under the existence of a moment map. As an application ofthis construction, we describe the phase space of a charged particle interacting witha Yang–Mills field. Finally, we introduce a singular analogue of this constructionand provide physical examples.The author is currently supported by the Spanish State Research Agency, through the SeveroOchoa and Mar ́ıa de Maetzu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M).Peer Reviewed20242024-12-1120252025-06-27journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/433042https://dx.doi.org/10.2436/20.2002.02.43reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4330422026-05-27T15:37:01Z
dc.title.none.fl_str_mv A promenade through singular symplectic geometry
title A promenade through singular symplectic geometry
spellingShingle A promenade through singular symplectic geometry
Nicolás Martínez, Pablo
Poisson geometry
Reduction
Minimal coupling
Lie algebroid
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::53 Differential geometry::53C Global differential geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short A promenade through singular symplectic geometry
title_full A promenade through singular symplectic geometry
title_fullStr A promenade through singular symplectic geometry
title_full_unstemmed A promenade through singular symplectic geometry
title_sort A promenade through singular symplectic geometry
dc.creator.none.fl_str_mv Nicolás Martínez, Pablo
author Nicolás Martínez, Pablo
author_facet Nicolás Martínez, Pablo
author_role author
dc.subject.none.fl_str_mv Poisson geometry
Reduction
Minimal coupling
Lie algebroid
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::53 Differential geometry::53C Global differential geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Poisson geometry
Reduction
Minimal coupling
Lie algebroid
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::53 Differential geometry::53C Global differential geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística
description https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.ca
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-12-11
2025
2025-06-27
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/433042
https://dx.doi.org/10.2436/20.2002.02.43
url https://hdl.handle.net/2117/433042
https://dx.doi.org/10.2436/20.2002.02.43
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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