The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories

Details The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories

2009-05-28

arxiv.org/abs/0905.4580v2

J.Geom.Phys.60:857-873,2010

Mathematics

Differential Geometry

29 pages, revised version as accepted for publication in J. Geom. Phys

Scientific paper

10.1016/j.geomphys.2010.02.003

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

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