2003/11/30 by Mauro Francaviglia, Marcella Palese, Ekkehart Winterroth
Physics and Astronomy · Mathematics · #math-ph #math.DG #math.MP #msc:53C05 #msc:58A20 #msc:70H05 #msc:37J05
published as Math. Publ. (Univ. Opava) 3 (2001) 415--424 · 9 pages, VIII Int. Conf. Diff. Geom. Appl. (Opava 2001); O. Kowalski et al. eds., misprints corrected
arxiv created 2004/05/28 · arxiv updated 2009/12/01
We 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.