Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds

Pages: 1 - 26, Volume 4, Issue 1, March 2012

doi:10.3934/jgm.2012.4.1       Abstract        References        Full Text (526.1K)       Related Articles

Cédric M. Campos - Dept. Matemática Fundamental, Universidad de La Laguna, ULL, Avda. Astrofísico Fco. Sánchez, 38206 La Laguna, Tenerife, Spain (email)
Elisa Guzmán - ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Dept. Matemática Fundamental, Universidad de La Laguna, ULL, Avda. Astrofísico Fco. Sánchez, 38206 La Laguna, Tenerife, Spain (email)
Juan Carlos Marrero - ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Dept. Matemática Fundamental, Universidad de La Laguna, ULL, Avda. Astrofísico Fco. Sánchez, 38206 La Laguna, Tenerife, Spain (email)

Abstract: 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.

Keywords:  Field theory, multisymplectic structure, Lagrangian submanifold, Tulczyjew's triple, Euler-Lagrange equation, Hamilton-De Donder-Weyl equation.
Mathematics Subject Classification:  Primary: 70S05; Secondary: 70H03, 70H05, 53D12.

Received: December 2011;      Revised: March 2012;      Published: April 2012.

 References