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

M. Palese·E. Winterroth
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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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M. Palese, E. Winterroth. 2005-01-02. Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles. https://arxiv.org/abs/math-ph/0311003

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