Physics – Mathematical Physics
Scientific paper
2003-11-05
Arch. Math. (Brno), 41(3) (2005) 289--310
Physics
Mathematical Physics
24 pages, minor changes, misprints corrected, a misprint in the coordinate expression of the Jacobi morphism corrected; final
Scientific paper
We derive both {\em local} and {\em global} generalized {\em Bianchi identities} for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the {\em a priori} introduction of a connection. The proof is based on a {\em global} decomposition of the {\em variational Lie derivative} of the generalized Euler--Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that {\em within} a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism {\em is not} intrinsically arbitrary. As a consequence the existence of {\em canonical} global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.
Palese Marcella
Winterroth Ekkehart
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