Variational Lie derivative and cohomology classes

Details Variational Lie derivative and cohomology classes Variational Lie derivative and cohomology classes

2011-03-02

arxiv.org/abs/1103.0434v1

Physics

Mathematical Physics

7 pages, XIX International Fall Workshop on Geometry and Physics, to appear in AIP Conf. Proc

Scientific paper

We relate cohomology defined by a system of local Lagrangian with the cohomology class of the system of local variational Lie derivative, which is in turn a local variational problem; we show that the latter cohomology class is zero, since the variational Lie derivative `trivializes' cohomology classes defined by variational forms. As a consequence, conservation laws associated with symmetries of the second variational derivative of a local variational problem are globally defined.

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