Conformal Killing tensors and covariant Hamiltonian dynamics.
Autor(a) principal: | |
---|---|
Data de Publicação: | 2014 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/4462 https://doi.org/10.1063/1.4902933 |
Resumo: | A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the H´enon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six. |
id |
UFOP_759ba4aefc82822e9437541882a4490e |
---|---|
oai_identifier_str |
oai:localhost:123456789/4462 |
network_acronym_str |
UFOP |
network_name_str |
Repositório Institucional da UFOP |
repository_id_str |
3233 |
spelling |
Cariglia, MarcoGibbons, G. W.Holten, J. W. vanHorvathy, P. A.Zhang, P. M.2015-02-23T15:29:39Z2015-02-23T15:29:39Z2014CARIGLIA, M. et al. Conformal Killing tensors and covariant Hamiltonian dynamics. Journal of Mathematical Physics, v. 55, p. 122702, 2014. Disponível em: <https://aip.scitation.org/doi/full/10.1063/1.4902933>. Acesso em: 20 fev. 2015. 0022-2488http://www.repositorio.ufop.br/handle/123456789/4462https://doi.org/10.1063/1.4902933A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the H´enon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.SymmetriesConserved quantitiesCovariant dynamicsConformal Killing tensors and covariant Hamiltonian dynamics.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO periódico Journal of Mathematical Physics permite o arquivamento da versão PDF do editor em repositórios institucionais após 12 meses de embargo. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=0022-2488>. Acesso em: 02 jan. 2017.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-82636http://www.repositorio.ufop.br/bitstream/123456789/4462/2/license.txtc2ffdd99e58acf69202dff00d361f23aMD52ORIGINALARTIGO_ConformalKillingTensors.pdfARTIGO_ConformalKillingTensors.pdfapplication/pdf304711http://www.repositorio.ufop.br/bitstream/123456789/4462/1/ARTIGO_ConformalKillingTensors.pdfa2afab633d5a980938afff0870ce825bMD51123456789/44622019-06-18 12:36:37.288oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-06-18T16:36:37Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
title |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
spellingShingle |
Conformal Killing tensors and covariant Hamiltonian dynamics. Cariglia, Marco Symmetries Conserved quantities Covariant dynamics |
title_short |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
title_full |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
title_fullStr |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
title_full_unstemmed |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
title_sort |
Conformal Killing tensors and covariant Hamiltonian dynamics. |
author |
Cariglia, Marco |
author_facet |
Cariglia, Marco Gibbons, G. W. Holten, J. W. van Horvathy, P. A. Zhang, P. M. |
author_role |
author |
author2 |
Gibbons, G. W. Holten, J. W. van Horvathy, P. A. Zhang, P. M. |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Cariglia, Marco Gibbons, G. W. Holten, J. W. van Horvathy, P. A. Zhang, P. M. |
dc.subject.por.fl_str_mv |
Symmetries Conserved quantities Covariant dynamics |
topic |
Symmetries Conserved quantities Covariant dynamics |
description |
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the H´enon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six. |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014 |
dc.date.accessioned.fl_str_mv |
2015-02-23T15:29:39Z |
dc.date.available.fl_str_mv |
2015-02-23T15:29:39Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CARIGLIA, M. et al. Conformal Killing tensors and covariant Hamiltonian dynamics. Journal of Mathematical Physics, v. 55, p. 122702, 2014. Disponível em: <https://aip.scitation.org/doi/full/10.1063/1.4902933>. Acesso em: 20 fev. 2015. |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/4462 |
dc.identifier.issn.none.fl_str_mv |
0022-2488 |
dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1063/1.4902933 |
identifier_str_mv |
CARIGLIA, M. et al. Conformal Killing tensors and covariant Hamiltonian dynamics. Journal of Mathematical Physics, v. 55, p. 122702, 2014. Disponível em: <https://aip.scitation.org/doi/full/10.1063/1.4902933>. Acesso em: 20 fev. 2015. 0022-2488 |
url |
http://www.repositorio.ufop.br/handle/123456789/4462 https://doi.org/10.1063/1.4902933 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFOP instname:Universidade Federal de Ouro Preto (UFOP) instacron:UFOP |
instname_str |
Universidade Federal de Ouro Preto (UFOP) |
instacron_str |
UFOP |
institution |
UFOP |
reponame_str |
Repositório Institucional da UFOP |
collection |
Repositório Institucional da UFOP |
bitstream.url.fl_str_mv |
http://www.repositorio.ufop.br/bitstream/123456789/4462/2/license.txt http://www.repositorio.ufop.br/bitstream/123456789/4462/1/ARTIGO_ConformalKillingTensors.pdf |
bitstream.checksum.fl_str_mv |
c2ffdd99e58acf69202dff00d361f23a a2afab633d5a980938afff0870ce825b |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP) |
repository.mail.fl_str_mv |
repositorio@ufop.edu.br |
_version_ |
1801685722482081792 |