Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents
We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of fo...
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Online Access: | https://doi.org/10.1515/cm-2016-0009 |
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doaj-86f0f20eb4a74044b0d9803394d84b692021-09-06T19:19:41ZengSciendoCommunications in Mathematics2336-12982016-12-0124212513510.1515/cm-2016-0009cm-2016-0009Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currentsPalese Marcella0Department of Mathematics, University of Torino, via C. Alberto 10, I-10123 Torino, ItalyWe will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local Noether strong currents are variationally equivalent to global canonical Noether currents. Variations, taken to be generalized symmetries and also belonging to the kernel of the second variational derivative of the local problem, generate canonical Noether currents - associated with variations of local Lagrangians - which in particular turn out to be conserved along any section. We also characterize the variation of the canonical Noether currents associated with a local variational problem.https://doi.org/10.1515/cm-2016-0009fibered manifoldjet spacelagrangian formalismvariational sequencesecond variational derivative. cohomologysymmetryconservation law |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Palese Marcella |
spellingShingle |
Palese Marcella Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents Communications in Mathematics fibered manifold jet space lagrangian formalism variational sequence second variational derivative. cohomology symmetry conservation law |
author_facet |
Palese Marcella |
author_sort |
Palese Marcella |
title |
Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents |
title_short |
Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents |
title_full |
Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents |
title_fullStr |
Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents |
title_full_unstemmed |
Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents |
title_sort |
variations by generalized symmetries of local noether strong currents equivalent to global canonical noether currents |
publisher |
Sciendo |
series |
Communications in Mathematics |
issn |
2336-1298 |
publishDate |
2016-12-01 |
description |
We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local Noether strong currents are variationally equivalent to global canonical Noether currents. Variations, taken to be generalized symmetries and also belonging to the kernel of the second variational derivative of the local problem, generate canonical Noether currents - associated with variations of local Lagrangians - which in particular turn out to be conserved along any section. We also characterize the variation of the canonical Noether currents associated with a local variational problem. |
topic |
fibered manifold jet space lagrangian formalism variational sequence second variational derivative. cohomology symmetry conservation law |
url |
https://doi.org/10.1515/cm-2016-0009 |
work_keys_str_mv |
AT palesemarcella variationsbygeneralizedsymmetriesoflocalnoetherstrongcurrentsequivalenttoglobalcanonicalnoethercurrents |
_version_ |
1717778066807193600 |