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

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

2003-11-11

arxiv.org/abs/math-ph/0311018v2

Math. Publ. (Univ. Opava) 3 (2001) 415--424

Physics

Mathematical Physics

9 pages, VIII Int. Conf. Diff. Geom. Appl. (Opava 2001); O. Kowalski et al. eds., misprints corrected

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A New Geometric Proposal for the Hamiltonian Description of Classical Field Theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A New Geometric Proposal for the Hamiltonian Description of Classical Field Theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A New Geometric Proposal for the Hamiltonian Description of Classical Field Theories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-421815