An alternative approach to the Cartan form in Lagrangian field theories. (English) Zbl 0652.58002

Saunders, D. J.

J. Phys. A 20, 339-349 (1987).

The present paper generalizes the idea of constructing an almost tangent structure on 2n-dimensional manifolds to jet bundles of a manifold. Then the author uses this structure to construct the Cartan form for Lagrangian field theories of first order and of higher order as well. The uniqueness of the constructed Cartan form is also studied. The conclusion is that the global Cartan form in higher-order field theories is not unique.

Reviewer: Z.Guo

MSC:

58A20	Jets in global analysis
70H20	Hamilton-Jacobi equations in mechanics

Keywords:

almost tangent structure; jet bundles; Lagrangian field theories