Article

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

12/2003;
Source: arXiv

ABSTRACT 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.

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### Keywords

corresponding generalized Jacobi morphism

gauge-natural bundles

gauge-natural invariant Lagrangian variational principle

generalized Bianchi identities

globally

infinitesimal principal automorphism {\em

{\em canonical} global superpotentials

{\em global} decomposition

{\em global} generalized {\em Bianchi identities}

{\em variational Lie derivative}