Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles. (English) Zbl 1112.58005

Palese, Marcella; Winterroth, Ekkehart

Arch. Math., Brno 41, No. 3, 289-310 (2005).

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.

Reviewer: Ivan Kolář (Brno)

MSC:

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

Keywords:

generalized Bianchi identities; Jacobi morphism