On a class of polynomial Lagrangians

Details On a class of polynomial Lagrangians On a class of polynomial Lagrangians

2001-11-09

arxiv.org/abs/math-ph/0111019v1

Rend.Circ.Mat.Palermo 66 (2001) 147-159

Physics

Mathematical Physics

LaTeX2e, amsmath, diagrams, hyperref; 15 pages

Scientific paper

In the framework of finite order variational sequences a new class of Lagrangians arises, namely, \emph{special} Lagrangians. These Lagrangians are the horizontalization of forms on a jet space of lower order. We describe their properties together with properties of related objects, such as Poincar\'e--Cartan and Euler--Lagrange forms, momenta and momenta of generating forms, a new geometric object arising in variational sequences. Finally, we provide a simple but important example of special Lagrangian, namely the Hilbert--Einstein Lagrangian.

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