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Gauge-natural PVPs, superpotentials and trivial Lagrangians. (English) Zbl 1344.58009

Iglesias Ponte, David (ed.) et al., Proceedings of the XV international workshop on geometry and physics, Puerto de la Cruz, Spain, September 11–16, 2006. Madrid: Real Sociedad Matemática Española (ISBN 978-84-935196-1-2/pbk). Publicaciones de la Real Sociedad Matemática Española 11, 231-236 (2007).
Summary: We define the superpotentials for gauge-natural Parametrized Variational Problems (PVPs). In view of a definition of augmented PVPs, we show that a pure divergence Lagrangian has trivial equations also in the case of PVPs but, as it happens in the free case, it has a non-vanishing superpotential. We compute it.
For the entire collection see [Zbl 1216.00039].

MSC:

58E30 Variational principles in infinite-dimensional spaces
49S05 Variational principles of physics
53C05 Connections (general theory)
58A20 Jets in global analysis
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
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