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Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles. (English) Zbl 1112.58005
The authors deduce the generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles without the a priori introduction of a connection. Their proof is based on a global decomposition of the variational Lie derivative of the generalized Euler-Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. Further, the existence of canonical global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.

58A20 Jets in global analysis
58A32 Natural bundles
58E30 Variational principles in infinite-dimensional spaces
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