Integrability and Dif feomorphisms on Target Space
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National Academy of Science of Ukraine
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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 dif feomorphisms. We classify the possible conservation
laws of field theories for the case of a three-dimensional target space. Further, we discuss
some explicit examples
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Adam, C., Sanchez-Guillen, J., & Wereszczynski, A. (2007). Integrability and Diffeomorphisms on Target Space. Symmetry, Integrability and Geometry: Methods and Applications. 3 (2007), 123, 11 pages
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https://doi.org/10.3842/SIGMA.2007.123Sponsors
A.W. gratefully acknowledges support from Adam Krzyzanowski Fund and Jagiellonian University (grant WRBW 41/07). C.A. and J.S.-G. thank MCyT (Spain) and FEDER (FPA2005-
01963), and support from Xunta de Galicia (grant PGIDIT06PXIB296182PR and Conselleria
de Educacion). Further, C.A. acknowledges support from the Austrian START award project
FWF-Y-137-TEC and from the FWF project P161 05 NO 5 of N.J. Mauser
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© 2007 Christoph Adam, Joaquin Sanchez-Guillen and Andrzej Wereszczynski. This work was published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License