We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the Hamiltonian field equations. In an analogous way to how these systems are defined in the so-called extended (symplectic) formulation of nonautonomous mechanics, we introduce Hamiltonian systems in the extended multimomentum bundle. The geometric properties of these systems are studied, the Hamiltonian equations are analyzed using integrable multivector fields, the corresponding variational principle is also stated, and the relation between the extended and the restricted Hamiltonian systems is established. All these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.
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November 2007
Research Article|
November 01 2007
Extended Hamiltonian systems in multisymplectic field theories
Arturo Echeverría-Enríquez;
Arturo Echeverría-Enríquez
Departamento de Matemática Aplicada IV,
Campus Norte UPC
, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona, Spain
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Manuel de León;
Manuel de León
a)
Instituto de Matemáticas y Física Fundamental,
CSIC
, C/Serrano 123, E-28006 Madrid, Spain
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Miguel C. Muñoz-Lecanda;
Miguel C. Muñoz-Lecanda
b)
Departamento de Matemática Aplicada IV,
Campus Norte UPC
, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona, Spain
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Narciso Román-Roy
Narciso Román-Roy
c)
Departamento de Matemática Aplicada IV,
Campus Norte UPC
, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona, Spain
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a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
c)
Electronic mail: [email protected]
J. Math. Phys. 48, 112901 (2007)
Article history
Received:
September 21 2006
Accepted:
October 02 2007
Citation
Arturo Echeverría-Enríquez, Manuel de León, Miguel C. Muñoz-Lecanda, Narciso Román-Roy; Extended Hamiltonian systems in multisymplectic field theories. J. Math. Phys. 1 November 2007; 48 (11): 112901. https://doi.org/10.1063/1.2801875
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