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arXiv · 1110.4778

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

Cédric M. Campos·Elisa Guzmán·Juan Carlos Marrero
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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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Cédric M. Campos, Elisa Guzmán, Juan Carlos Marrero. 2011-10-21. Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds. https://doi.org/10.3934/jgm.2012.4.1

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