A New geometric proposal for the Hamiltonian description of classical field theories
Nov, 2003
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Abstract:
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 --forms, where 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 --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.- talk: Opava 2001/08/27
- field theory: classical
- Hamiltonian formalism
- differential forms: symplectic
- differential geometry
- operator: differential
- fibre bundle
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