Non-relativistic conformal symmetries in fluid mechanics
Abstract
The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schroedinger group, which also involves, in addition, Schroedinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally-invariant relativistic theory, the recently discussed Conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.
Keywords
Cite
@article{arxiv.0906.3594,
title = {Non-relativistic conformal symmetries in fluid mechanics},
author = {P. -M. Zhang and P. A. Horvathy},
journal= {arXiv preprint arXiv:0906.3594},
year = {2010}
}
Comments
Substantially revised and extended version. A new Section is added on deriving the non-relativistic fluid mechanics from relativistic conformal field theory. The breaking of Conformal Galilei symmetry (obtained by contraction) is explained by the subtle behavior of the non-relativistic limit. 18 pages no figures. Some more references added