CLASSICAL FIELD THEORIES OF FIRST ORDER AND LAGRANGIAN SUBMANIFOLDS OF PREMULTISYMPLECTIC MANIFOLDS

被引：11

作者：

Campos, Cedric M. ^{[1
]}

Guzman, Elisa ^{[1
]}

Carlos Marrero, Juan ^{[1
]}

机构：

[1] Univ La Laguna, Dept Matemat Fundamental, ULL CSIC Geometria Diferencial & Mecan Geometr, E-38206 Tenerife, Spain

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2012年 / 4卷 / 01期

关键词：

Field theory; multisymplectic structure; Lagrangian submanifold; Tulczyjew's triple; Euler-Lagrange equation; Hamilton-De Donder-Weyl equation; GEOMETRY; EQUATIONS; SYSTEMS; MAPS;

D O I：

10.3934/jgm.2012.4.1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a fibration is discussed. The triple is adapted to the extended Hamiltonian formalism. Using this triple, we prove that Euler-Lagrange and Hamilton-De Donder-Weyl equations are the local equations defining Lagrangian submanifolds of a premultisymplectic manifold.

引用

页码：1 / 26

页数：26

共 50 条

[1] Lagrangian constraint analysis of first-order classical field theories with an application to gravity
Diez, Veronica Errasti
Maier, Markus
Mendez-Zavaleta, Julio A.
Tehrani, Mojtaba Taslimi
PHYSICAL REVIEW D, 2020, 102 (06):
[2] Lagrangian submanifolds in para-Kahler manifolds
Chen, Bang-Yen
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (11) : 3561 - 3571
[3] Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
Andres, E. Garcia-Torano
Guzman, E.
Marrero, J. C.
Mestdag, T.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (22)
[4] The Lagrangian-Hamiltonian formalism for higher order field theories
Vitagliano, Luca
JOURNAL OF GEOMETRY AND PHYSICS, 2010, 60 (6-8) : 857 - 873
[5] Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
Roman-Roy, Narciso
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2009, 5
[6] Unambiguous formalism for higher order Lagrangian field theories
Campos, Cedric M.
de Leon, Manuel
Martin de Diego, David
Vankerschaver, Joris
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (47)
[7] Constrained variational calculus for higher order classical field theories
Campos, Cedric M.
de Leon, Manuel
Martin de Diego, David
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (45)
[8] A NEW MULTISYMPLECTIC UNIFIED FORMALISM FOR SECOND ORDER CLASSICAL FIELD THEORIES
Daniel Prieto-Martinez, Pedro
Roman-Roy, Narciso
JOURNAL OF GEOMETRIC MECHANICS, 2015, 7 (02): : 203 - 253
[9] LAGRANGIAN H-UMBILICAL SUBMANIFOLDS OF PARA-KAHLER MANIFOLDS
Chen, Bang-Yen
TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (06): : 2483 - 2502
[10] Time-dependent mechanics and Lagrangian submanifolds of presymplectic and Poisson manifolds
Guzman, E.
Marrero, J. C.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (50)

← 1 2 3 4 5 →