Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles

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.