Superpotentials in Variational Sequences

M. Francaviglia, M. Palese, R. Vitolo


Abstract. In the Lagrangian approach to conservation laws of field theories one defines a suitable vector density which generates the {\em conserved Noether currents\/}. As it is known, in {\em natural\/} (and {\em gauge--natural\/}) field theories, along any section this density is the divergence of a skew--symmetric tensor density, which is called a {\em superpotential} for the conserved quantity. Making use of some abstract results due to Hor\'ak and Kol\' a\v{r}, in this paper we give a geometrical interpretation of superpotentials in the framework of variational sequences according to Krupka. We refer to our previous results on {\em variational Lie derivatives\/} concerning abstract versions of Noether's theorems, which are here interpreted in terms of conserved currents.

AMSclassification. 58A12, 58A20, 58E30, 58G05, 70H33, 83E99

Keywords. Fibered manifold, jet space, variational sequence, symmetries, conservation laws, superpotentials