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...

Full description

Bibliographic Details
Main Authors: Christoph Adam, Joaquin Sanchez-Guillen, Andrzej Wereszczynski
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2007-12-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Online Access:http://www.emis.de/journals/SIGMA/2007/123/
_version_ 1811342786378596352
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