Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 123, 11 pages      arXiv:0712.3385
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Integrability and Diffeomorphisms on Target Space

Christoph Adam a, Joaquin Sanchez-Guillen a and Andrzej Wereszczynski b
a) Department of Particle Physics, University of Santiago de Compostela, Spain
b) Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow, Poland

Received October 18, 2007, in final form December 10, 2007; Published online December 20, 2007

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.

Key words: integrability; zero curvature; conservation laws; nonlinear field theories.

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