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Hamiltonian Systems in Multisymplectic Field Theories

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Echeverría Enríquez, Arturo
León, Manuel de
Muñoz Lecanda, Miguel CarlosMés informacióMés informació
Román Roy, NarcisoMés informacióMés informacióMés informació
Document typeArticle
Defense date2005-06-20
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 2.5 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 2.5 Spain
Abstract
We consider Hamiltonian systems in first-order multisymplectic field theories. First we review the construction and properties of Hamiltonian systems in the so-called restricted multimomentum bundle using Hamiltonian sections, including the variational principle which leads to the Hamiltonian field equations. Then, we introduce Hamiltonian systems in the extended multimomentum bundle, in an analogous way to how these systems are defined in non-autonomous (symplectic) mechanics or in the so-called extended (symplectic) formulation of autonomous mechanics. The corresponding variational principle is also stated for these extended Hamiltonian systems and, after studying the geometric properties of these systems, we establish the relation between the extended and the restricted ones. These definitions and properties are also adapted to submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.
URIhttp://hdl.handle.net/2117/399
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