×

Variational Lie derivative and cohomology classes. (English) Zbl 1276.70012

Herdeiro, Carlos (ed.) et al., XIX international fall workshop on geometry and physics, Porto, Portugal, September 6–9, 2010. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0918-7/pbk). AIP Conference Proceedings 1360, 106-112 (2011).
Summary: We relate the 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.
For the entire collection see [Zbl 1228.81023].

MSC:

70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
58E30 Variational principles in infinite-dimensional spaces
PDFBibTeX XMLCite
Full Text: DOI arXiv