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Zbl 1210.70025
Echeverr\'ia-Enr\'iquez, Arturo; de León, Manuel; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
Extended Hamiltonian formalism of field theories: variational aspects and other topics. (English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2--10, 2005. Sofia: Bulgarian Academy of Sciences. 116-127 (2006). ISBN 954-8495-30-9/pbk

Summary: We consider Hamiltonian systems in first-order multisymplectic field theories. In particular, we introduce Hamiltonian systems in the extended multimomentum bundle. The resulting extended Hamiltonian formalism is the generalization to field theories of the extended (symplectic) formalism for non-autonomous mechanical systems. In order to derive the corresponding field equations, a variational principle is stated for these extended Hamiltonian systems and, after studying the geometric properties of these systems, we establish the relation between this extended formalism and the standard one.

MSC 2000:: *70S05 Lagrangian formalism and Hamiltonian formalism
58E30 Variational principles on infinite-dimensional spaces
70G45 Differential-geometric methods

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