Summary: We specialize in a new way the second Noether theorem for gauge-natural field theories by relating it to the Jacobi morphism and show that it plays a fundamental role in the derivation of canonical covariant conserved quantities. In particular we show that Bergmann-Bianchi identities for such theories hold true covariantly and canonically only along solutions of generalized gauge-natural Jacobi equations. Vice versa, all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms lying in the kernel of generalized Jacobi morphisms satisfy Bergmann-Bianchi identities and thus are generators of canonical covariant currents and superpotentials. As a consequence of the second Noether theorem, we further show that there exists a covariantly conserved current associated with the Lagrangian obtained by contracting the Euler-Lagrange morphism with a gauge-natural Jacobi vector field. We use as fundamental tools an invariant decomposition formul!

EUDML-ID : urn:eudml:doc:219871
Mots clés:

@article{701775,
     title = {Gauge-natural field theories and Noether theorems: canonical covariant conserved currents},
     booktitle = {Proceedings of the 25th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2006},
     pages = {[161]-174},
     mrnumber = {MR2287135},
     zbl = {1113.58002},
     url = {http://dml.mathdoc.fr/item/701775}
}

Palese, Marcella; Winterroth, Ekkehart. Gauge-natural field theories and Noether theorems: canonical covariant conserved currents, dans Proceedings of the 25th Winter School "Geometry and Physics", GDML_Books,  (2006), pp. [161]-174. http://gdmltest.u-ga.fr/item/701775/