Classical Field theory on Lie algebroids: multisymplectic formalism

Details Classical Field theory on Lie algebroids: multisymplectic formalism Classical Field theory on Lie algebroids: multisymplectic formalism

2004-11-16

arxiv.org/abs/math/0411352v1

Mathematics

Differential Geometry

43 pages

Scientific paper

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a Lagrangian function is given, we find the equations of motion in terms of a Cartan form canonically associated to the Lagrangian. The Hamiltonian formalism is also extended to this setting and we find the relation between the solutions of both formalism. When the first Lie algebroid is a tangent bundle we give a variational description of the equations of motion. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), variational problems for holomorphic maps, Sigma models or Chern-Simons theories. One of the advantages of our theory is that it is based in the existence of a multisymplectic form on a Lie algebroid.

Affiliated with

Also associated with

No associations

Rating

Classical Field theory on Lie algebroids: multisymplectic formalism 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 Classical Field theory on Lie algebroids: multisymplectic formalism, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical Field theory on Lie algebroids: multisymplectic formalism will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212492