TY - JOUR
T1 - The second-order problem for k-presymplectic Lagrangian field theories
T2 - application to the Einstein–Palatini model
AU - Adame-Carrillo, David
AU - Gaset, Jordi
AU - Román-Roy, Narciso
N1 - Funding Information:
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.
Publisher Copyright:
© 2021, The Author(s).
PY - 2022/1
Y1 - 2022/1
N2 - 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.
AB - 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.
KW - Classical field theories
KW - Einstein–Palatini model
KW - k-symplectic manifolds
KW - Lagrangian formalism
UR - http://www.scopus.com/inward/record.url?scp=85117338092&partnerID=8YFLogxK
U2 - 10.1007/s13398-021-01136-x
DO - 10.1007/s13398-021-01136-x
M3 - Article
AN - SCOPUS:85117338092
VL - 116
JO - REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A: MATEMATICAS
JF - REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A: MATEMATICAS
SN - 1578-7303
IS - 1
M1 - 20
ER -