Geodesic
Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles
Archivum mathematicum, Tome 41 (2005) no. 3, pp. 289-310

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We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The 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. In particular, we show that within a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism is not intrinsically arbitrary. As a consequence the existence of canonical global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.
Classification : 58A20, 58A32, 58E30, 58J70
Keywords: jets; gauge-natural bundles; variational principles; generalized Bianchi identities; Jacobi morphisms; invariance and symmetry properties 
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     title = {Global generalized {Bianchi} identities for invariant variational problems on gauge-natural bundles},
     journal = {Archivum mathematicum},
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     volume = {41},
     number = {3},
     year = {2005},
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     zbl = {1112.58005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005__41_3_a5/}
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Palese, Marcella; Winterroth, Ekkehart. Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles. Archivum mathematicum, Tome 41 (2005) no. 3, pp. 289-310. http://geodesic.mathdoc.fr/item/ARM_2005__41_3_a5/