Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles
Palese, M. ; Winterroth, E.
arXiv, 0311003 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-11-05
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Mathematics - Differential Geometry,  58A20,  58A32,  58E30,  58E40,  58J10,  58J70 
@article{0311003,
     author = {Palese, M. and Winterroth, E.},
     title = {Global Generalized Bianchi Identities for Invariant Variational Problems
  on Gauge-natural Bundles},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0311003}
}

Palese, M.; Winterroth, E. Global Generalized Bianchi Identities for Invariant Variational Problems
  on Gauge-natural Bundles. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0311003/