Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles

Palese, Marcella ; Winterroth, Ekkehart

Archivum mathematicum, Tome 41 (2005) no. 3, pp. 289-310

Abstract (VO)

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.

Détail

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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