Variational derivatives in locally Lagrangian field theories and Noether--Bessel-Hagen currents

Abstract

The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application we determine the condition for a Noether--Bessel-Hagen current, associated with a generalized symmetry, to be variationally equivalent to a Noether current for an invariant Lagrangian. We show that, if it exists, this Noether current is exact on-shell and generates a canonical conserved quantity.

20 pages

References in corpus (2)

• Variationally equivalent problems and variations of Noether currents
• Cohomological obstructions in locally variational field theories

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• A cohomological obstruction in higher dimensional Chern--Simons gauge theories