Extended Hamiltonian formalism of field theories: variational aspects and other topics. (English) Zbl 1210.70025

Echeverría-Enríquez, Arturo; de León, Manuel; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso

Mladenov, Ivaïlo (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 (ISBN 954-8495-30-9/pbk). 116-127 (2006).

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.
For the entire collection see [Zbl 1089.53004].

MSC:

70S05	Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
58E30	Variational principles in infinite-dimensional spaces
70G45	Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics