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Extended Hamiltonian systems in multisymplectic field theories
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
non-autonomous 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.Comment: 36 pp. The introduction and the abstract have been rewritten. New
references are added and some little mistakes are corrected. The title has
been slightly modifie