Integrability and Diffeomorphisms on Target Space
We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, gen...
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Format: | Article |
Language: | English |
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National Academy of Science of Ukraine
2007-12-01
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Series: | Symmetry, Integrability and Geometry: Methods and Applications |
Subjects: | |
Online Access: | http://www.emis.de/journals/SIGMA/2007/123/ |
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author | Christoph Adam Joaquin Sanchez-Guillen Andrzej Wereszczynski |
author_facet | Christoph Adam Joaquin Sanchez-Guillen Andrzej Wereszczynski |
author_sort | Christoph Adam |
collection | DOAJ |
description | We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving diffeomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit examples. |
first_indexed | 2024-04-13T19:17:07Z |
format | Article |
id | doaj.art-b0acaed1f9514ca48f63991cb611d967 |
institution | Directory Open Access Journal |
issn | 1815-0659 |
language | English |
last_indexed | 2024-04-13T19:17:07Z |
publishDate | 2007-12-01 |
publisher | National Academy of Science of Ukraine |
record_format | Article |
series | Symmetry, Integrability and Geometry: Methods and Applications |
spelling | doaj.art-b0acaed1f9514ca48f63991cb611d9672022-12-22T02:33:38ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-12-013123Integrability and Diffeomorphisms on Target SpaceChristoph AdamJoaquin Sanchez-GuillenAndrzej WereszczynskiWe briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving diffeomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit examples.http://www.emis.de/journals/SIGMA/2007/123/integrabilityzero curvatureconservation lawsnonlinear field theories |
spellingShingle | Christoph Adam Joaquin Sanchez-Guillen Andrzej Wereszczynski Integrability and Diffeomorphisms on Target Space Symmetry, Integrability and Geometry: Methods and Applications integrability zero curvature conservation laws nonlinear field theories |
title | Integrability and Diffeomorphisms on Target Space |
title_full | Integrability and Diffeomorphisms on Target Space |
title_fullStr | Integrability and Diffeomorphisms on Target Space |
title_full_unstemmed | Integrability and Diffeomorphisms on Target Space |
title_short | Integrability and Diffeomorphisms on Target Space |
title_sort | integrability and diffeomorphisms on target space |
topic | integrability zero curvature conservation laws nonlinear field theories |
url | http://www.emis.de/journals/SIGMA/2007/123/ |
work_keys_str_mv | AT christophadam integrabilityanddiffeomorphismsontargetspace AT joaquinsanchezguillen integrabilityanddiffeomorphismsontargetspace AT andrzejwereszczynski integrabilityanddiffeomorphismsontargetspace |