Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds
Cédric M. Campos - 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.
Received: December 2011; Revised: March 2012; Published: April 2012.
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