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

Cédric M. Campos; Elisa Guzmán; Juan Carlos Marrero

doi:10.3934/jgm.2012.4.1

Article Contents

2012, Volume 4, Issue 1: 1-26. Doi: 10.3934/jgm.2012.4.1

This issue Previous Article Next Article Homogeneity and projective equivalence of differential equation fields

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

1.
Dept. Matemática Fundamental, Universidad de La Laguna, ULL, Avda. Astrofísico Fco. Sánchez, 38206 La Laguna, Tenerife
2.
ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Dept. Matemática Fundamental, Universidad de La Laguna, ULL, Avda. Astrofísico Fco. Sánchez, 38206 La Laguna, Tenerife

Received: November 30, 2011

Revised: February 29, 2012

Published: February 2012

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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.

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Mathematics Subject Classification: Primary: 70S05; Secondary: 70H03, 70H05, 53D12.

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References

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