Poisson–Poincaré reduction for Field Theories

Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we study the reduction of this formulation to obtain an analogue...

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Detalles Bibliográficos
Autores: Berbel López, Miguel Ángel, Castrillón López, Marco
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/72668
Acceso en línea:https://hdl.handle.net/20.500.14352/72668
Access Level:acceso abierto
Palabra clave:51-7
Field theory
Symmetries
Covariant reduction
Poisson bracket
Polysymplectic
Multisymplectic
Poisson–Poincaré
Física matemática
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spelling Poisson–Poincaré reduction for Field TheoriesBerbel López, Miguel ÁngelCastrillón López, Marco51-7Field theorySymmetriesCovariant reductionPoisson bracketPolysymplecticMultisymplecticPoisson–PoincaréFísica matemáticaGiven a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we study the reduction of this formulation to obtain an analogue of Poisson–Poincaré reduction for field theories. This procedure is related to the Lagrange–Poincaré reduction for field theories via a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.Universidad Complutense de Madrid20222022-10-2720222022-10-27journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://hdl.handle.net/20.500.14352/72668reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/726682026-06-02T12:44:21Z
dc.title.none.fl_str_mv Poisson–Poincaré reduction for Field Theories
title Poisson–Poincaré reduction for Field Theories
spellingShingle Poisson–Poincaré reduction for Field Theories
Berbel López, Miguel Ángel
51-7
Field theory
Symmetries
Covariant reduction
Poisson bracket
Polysymplectic
Multisymplectic
Poisson–Poincaré
Física matemática
title_short Poisson–Poincaré reduction for Field Theories
title_full Poisson–Poincaré reduction for Field Theories
title_fullStr Poisson–Poincaré reduction for Field Theories
title_full_unstemmed Poisson–Poincaré reduction for Field Theories
title_sort Poisson–Poincaré reduction for Field Theories
dc.creator.none.fl_str_mv Berbel López, Miguel Ángel
Castrillón López, Marco
author Berbel López, Miguel Ángel
author_facet Berbel López, Miguel Ángel
Castrillón López, Marco
author_role author
author2 Castrillón López, Marco
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-7
Field theory
Symmetries
Covariant reduction
Poisson bracket
Polysymplectic
Multisymplectic
Poisson–Poincaré
Física matemática
topic 51-7
Field theory
Symmetries
Covariant reduction
Poisson bracket
Polysymplectic
Multisymplectic
Poisson–Poincaré
Física matemática
description Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we study the reduction of this formulation to obtain an analogue of Poisson–Poincaré reduction for field theories. This procedure is related to the Lagrange–Poincaré reduction for field theories via a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-10-27
2022
2022-10-27
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/72668
url https://hdl.handle.net/20.500.14352/72668
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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