The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model

David Adame-Carrillo; Jordi Gaset; Narciso Román-Roy

doi:10.1007/s13398-021-01136-x

The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model

David Adame-Carrillo, Jordi Gaset, Narciso Román-Roy^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

4 Citations (Scopus)

78 Downloads (Pure)

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.

Original language	English
Article number	20
Number of pages	25
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A: Matematicas
Volume	116
Issue number	1
DOIs	https://doi.org/10.1007/s13398-021-01136-x
Publication status	Published - Jan 2022
MoE publication type	A1 Journal article-refereed

Funding

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.

Keywords

Classical field theories
Einstein–Palatini model
k-symplectic manifolds
Lagrangian formalism

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10.1007/s13398-021-01136-x

Adame-Carrillo_The second-order problem for k-presymplectic Lagrangian field theoriesFinal published version, 397 KBLicence: CC BY

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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.",

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The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model. / Adame-Carrillo, David; Gaset, Jordi; Román-Roy, Narciso.
In: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A: Matematicas, Vol. 116, No. 1, 20, 01.2022.

Research output: Contribution to journal › Article › Scientific › peer-review

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AU - Román-Roy, Narciso

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The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model

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