Variational Lie derivative and cohomology classes
arXiv:1103.0434 · doi:10.1063/1.3599134
Abstract
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 ensuring the vanishing of the second variational derivative of a local variational problem are globally defined.
7 pages, misprints in Corollary 2 and a misleading in the abstract and the introduction corrected, XIX International Fall Workshop on Geometry and Physics