Gauge-natural field theories and Noether theorems: canonical covariant conserved currents

Palese, Marcella, and Winterroth, Ekkehart. "Gauge-natural field theories and Noether theorems: canonical covariant conserved currents." Proceedings of the 25th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2006. [161]-174. <http://eudml.org/doc/219871>.

@inProceedings{Palese2006,
abstract = {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!},
author = {Palese, Marcella, Winterroth, Ekkehart},
booktitle = {Proceedings of the 25th Winter School "Geometry and Physics"},
location = {Palermo},
pages = {[161]-174},
publisher = {Circolo Matematico di Palermo},
title = {Gauge-natural field theories and Noether theorems: canonical covariant conserved currents},
url = {http://eudml.org/doc/219871},
year = {2006},
}

TY - CLSWK
AU - Palese, Marcella
AU - Winterroth, Ekkehart
TI - Gauge-natural field theories and Noether theorems: canonical covariant conserved currents
T2 - Proceedings of the 25th Winter School "Geometry and Physics"
PY - 2006
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [161]
EP - 174
AB - 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!
UR - http://eudml.org/doc/219871
ER -