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Conservation Laws and Variational Sequences in Gauge-Natural Theories | | L. Fatibene
; M. Francaviglia
; M. Palese
; | | Date: |
19 Nov 2003 | | Journal: | Math.Proc.Cambridge Phil.Soc. 130 (2001) 555-569 | | Subject: | Mathematical Physics; Differential Geometry MSC-class: 58A12;58A20;58E30;58Z05;70H33;83E99 | math-ph math.DG math.MP | | Affiliation: | Dept. Math. Univ. of Torino, Italy | | Abstract: | 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 Koláv{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. | | Source: | arXiv, math-ph/0311028 | | Services: | Forum | Review | PDF | Favorites | |
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