Symmetries of Helmholtz forms and globally variational dynamical forms

Details Symmetries of Helmholtz forms and globally variational dynamical forms Symmetries of Helmholtz forms and globally variational dynamical forms

2011-10-26

arxiv.org/abs/1110.5764v1

Physics

Mathematical Physics

Presented at QTS7 - Quantum Theory and Symmetries VII, Prague 7-13/08/2011

Scientific paper

Invariance properties of classes in the variational sequence suggested to Krupka et al. the idea that there should exist a close correspondence between the notions of variationality of a differential form and invariance of its exterior derivative. It was shown by them that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form, so that the latter is locally the Euler--Lagrange form of a Lagrangian. We show that the corresponding local system of Euler--Lagrange forms is variationally equivalent to a global Euler--Lagrange form.

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