2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95245We 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.24 pages, minor changes, misprints corrected, a misprint in the coordinate expression of the Jacobi morphism corrected; final version to appear in Arch. Math. (Brno)Mathematical PhysicsHigh Energy Physics - TheoryDifferential Geometry58A20;58A32;58E30;58E40;58J10;58J70text