Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles

Marcella Palese; Ekkehart Winterroth

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 3, page 289-310
  • ISSN: 0044-8753

Abstract

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We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The 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. In particular, we show that within a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism is not intrinsically arbitrary. As a consequence the existence of canonical global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.

How to cite

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Palese, Marcella, and Winterroth, Ekkehart. "Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles." Archivum Mathematicum 041.3 (2005): 289-310. <http://eudml.org/doc/249500>.

@article{Palese2005,
abstract = {We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The 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. In particular, we show that within a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism is not intrinsically arbitrary. As a consequence the existence of canonical global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.},
author = {Palese, Marcella, Winterroth, Ekkehart},
journal = {Archivum Mathematicum},
keywords = {jets; gauge-natural bundles; variational principles; generalized Bianchi identities; Jacobi morphisms; invariance and symmetry properties; generalized Bianchi identities; Jacobi morphism},
language = {eng},
number = {3},
pages = {289-310},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles},
url = {http://eudml.org/doc/249500},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Palese, Marcella
AU - Winterroth, Ekkehart
TI - Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 3
SP - 289
EP - 310
AB - We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The 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. In particular, we show that within a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism is not intrinsically arbitrary. As a consequence the existence of canonical global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.
LA - eng
KW - jets; gauge-natural bundles; variational principles; generalized Bianchi identities; Jacobi morphisms; invariance and symmetry properties; generalized Bianchi identities; Jacobi morphism
UR - http://eudml.org/doc/249500
ER -

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