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 36 条

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Roman-Roy N., ARXIVMATHPH0602038

[32] ON THE k-SYMPLECTIC, k-COSYMPLECTIC AND MULTISYMPLECTIC FORMALISMS OF CLASSICAL FIELD THEORIES [J].