Complex Generated by Variational Derivatives. Lagrangian Formalism of Infinite Order and a Generalized Stokes' Formula

Details Complex Generated by Variational Derivatives. Lagrangian Formalism of Infinite Order and a Generalized Stokes' Formula Complex Generated by Variational Derivatives. Lagrangian Formalism of Infinite Order and a Generalized Stokes' Formula

1997-11-18

arxiv.org/abs/dg-ga/9711013v1

Uspekhi Mat. Nauk 51 (6) (1996), 195-196

Mathematics

Differential Geometry

LaTeX, 4 pages

Scientific paper

We prove that an analog of the exterior differential acts on the space of
arbitrary Lagrangians of multidimensional paths on any manifold or
supermanifold, thus making this space into a cochain complex. An analog of the
Stokes' formula holds. The construction and the proofs are purely geometrical,
in terms of the variation of corresponding actions.

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