A New Geometric Proposal for the Hamiltonian Description of Classical Field Theories

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dc.creatorFrancaviglia, Mauro
dc.creatorPalese, Marcella
dc.creatorWinterroth, Ekkehart
dc.date2003-11-11
dc.date2004-05-28
dc.date.accessioned2026-07-07T04:30:43Z
dc.date.available2026-07-07T04:30:43Z
dc.descriptionWe consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory are defined in terms of multisymplectic $(n+2)$--forms, where $n$ is the dimension of the basis manifold, together with connections on the configuration bundle. We provide a new geometric Hamiltonian description of field theory, based on the introduction of a suitable {\em composite fibered bundle} which plays the role of an {\em extended configuration bundle}. Instead of fibrations over an $n$--dimensional base manifold $\bX$, we consider {\em fibrations over a line bundle $\Tht$ fibered over $\bX$}. The concepts of {\em extended Legendre bundle}, {\em Hamiltonian connection}, {\em Hamiltonian form} and {\em covariant Hamilton equations} are introduced and put in relation with the corresponding standard concepts in the polymomentum approach to field theory.
dc.description9 pages, VIII Int. Conf. Diff. Geom. Appl. (Opava 2001); O. Kowalski et al. eds., misprints corrected
dc.identifierhttps://arxiv.org/abs/math-ph/0311018
dc.identifierhttp://arxiv.org/abs/math-ph/0311018
dc.identifierMath. Publ. (Univ. Opava) 3 (2001) 415--424
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57560
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subject53C05;58A20;70H05;37J05
dc.titleA New Geometric Proposal for the Hamiltonian Description of Classical Field Theories
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