Symmetries of Helmholtz forms and globally variational dynamical forms

Abstract

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.

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

References in corpus (8)

• Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)
• Noether's second theorem in a general setting. Reducible gauge theories
• Covariant gauge-natural conservation laws
• The Hessian and Jacobi Morphisms for Higher Order Calculus of Variations
• Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles
• Conservation laws for non global Lagrangians
• Noether conservation laws issue from the gauge invariance of an Euler-Lagrange operator, but not a Lagrangian
• Variational Lie derivative and cohomology classes

Cited by in corpus (3)

• Variational Sequences, Representation Sequences and Applications in Physics
• Variational derivatives in locally Lagrangian field theories and Noether--Bessel-Hagen currents
• Cohomological obstructions in locally variational field theories