Physics – Mathematical Physics
Scientific paper
2003-11-19
Math.Proc.Cambridge Phil.Soc.130:555-569,2001
Physics
Mathematical Physics
16 pages, slightly revised version of a paper appeared in Math. Proc. Camb. Phil. Soc
Scientific paper
10.1017/S0305004101004881
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant gauge--natural bundle this density is the divergence of a skew--symmetric (tensor) density, which is called a {\em superpotential} for the conserved currents. We describe gauge--natural superpotentials in the framework of finite order variational sequences according to Krupka. We refer to previous results of ours on {\em variational Lie derivatives} concerning abstract versions of Noether's theorems, which are here interpreted in terms of ``horizontal'' and ``vertical'' conserved currents. The gauge--natural lift of principal automorphisms implies suitable linearity properties of the Lie derivative operator. Thus abstract results due to Kol\'a\v{r}, concerning the integration by parts procedure, can be applied to prove the {\em existence} and {\em globality} of superpotentials in a very general setting.
Fatibene Lorenzo
Francaviglia Mauro
Palese Marcella
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