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.

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

PALESE, Marcella;WINTERROTH, Ekkehart Hans Konrad
2016

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.
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http://arxiv.org/abs/1601.07193
Mathematical Physics; Mathematical Physics; Mathematics - Mathematical Physics; 58A20, 58E30, 46M18
Francesco, Cattafi; Marcella, Palese; Ekkehart, Winterroth
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1551849
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