Address.
Department of Mathematics,
University of Torino,
Via C. Alberto 10, 10123 Torino, Italy
E-mail. palese@dm.unito.it ekkehart@dm.unito.it
Abstract.
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.
AMSclassification. 58A20, 58A32, 58E30, 58E40, 58J10, 58J70.
Keywords. Jets, gauge-natural bundles, variational principles, generalized Bianchi identities, Jacobi morphisms, invariance and symmetry properties.