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

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

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