Integrability and diffeomorphisms on target space

DOI10.3842/SIGMA.2007.123zbMATH Open1134.37026arXiv0712.3385WikidataQ112234567 ScholiaQ112234567MaRDI QIDQ2473533

Joaquín Sánchez Guillén, Christoph Adam, Andrzej Wereszczynski

Publication date: 27 February 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/0712.3385

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zbMATH Keywords

conservation lawszero curvaturenonlinear field theories

Mathematics Subject Classification ID

Model quantum field theories (81T10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

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