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The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model
dc.contributor.author | Adame Carrillo, David |
dc.contributor.author | Gaset Rifà, Jordi |
dc.contributor.author | Román Roy, Narciso |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2022-04-05T07:48:35Z |
dc.date.available | 2022-04-05T07:48:35Z |
dc.date.issued | 2022-01-01 |
dc.identifier.citation | Adame, D.; Gaset, J.; Roman-Roy, N. The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model. "Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas", 1 Gener 2022, vol. 116, núm. article 20. |
dc.identifier.issn | 1579-1505 |
dc.identifier.uri | http://hdl.handle.net/2117/365264 |
dc.description | The version of record of this article, first published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, is available online at Publisher’s website: http://dx.doi.org/10.1007/s13398-021-01136-x |
dc.description.abstract | In general, the system of 2nd-order partial differential equations made of the Euler–Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of this work is to develop a fully geometric constraint algorithm which allows us to find a submanifold where the Euler–Lagrange equations have solution, and split the constraints into two kinds depending on their origin. We do so using k-symplectic geometry, which is the simplest intrinsic description of classical field theories. As a second aim, the Einstein–Palatini model of General Relativity is studied using this algorithm. |
dc.description.sponsorship | We acknowledge the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades project PGC2018-098265-B-C33 and the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017-SGR-932. |
dc.format.extent | 25 p. |
dc.language.iso | eng |
dc.publisher | springer-Verlag |
dc.rights | Attribution 4.0 International |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
dc.subject | Àrees temàtiques de la UPC::Física |
dc.subject.lcsh | Symplectic geometry |
dc.subject.lcsh | Field theory (Physics) |
dc.subject.lcsh | General relativity (Physics) |
dc.subject.other | Classical field theories |
dc.subject.other | k-symplectic manifolds |
dc.subject.other | Lagrangian formalism |
dc.subject.other | Einstein–Palatini model |
dc.title | The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model |
dc.type | Article |
dc.subject.lemac | Geometria simplèctica |
dc.subject.lemac | Camps, Teoria dels (Física) |
dc.subject.lemac | Relativitat general (Física) |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.identifier.doi | 10.1007/s13398-021-01136-x |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry |
dc.subject.ams | Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories |
dc.subject.ams | Classificació AMS::83 Relativity and gravitational theory::83C General relativity |
dc.relation.publisherversion | https://link.springer.com/article/10.1007%2Fs13398-021-01136-x |
dc.rights.access | Open Access |
local.identifier.drac | 32367058 |
dc.description.version | Postprint (published version) |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-098265-B-C33/ES/GEOMETRIA-FISICA-CONTROL Y APLICACIONES/ |
local.citation.author | Adame, D.; Gaset, J.; Roman-Roy, N. |
local.citation.publicationName | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas |
local.citation.volume | 116 |
local.citation.number | 1 |
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