Eur. Phys. J. C (2010) 65: 607-614
https://doi.org/10.1140/epjc/s10052-009-1221-x

Regular Article - Theoretical Physics

Non-relativistic conformal symmetries in fluid mechanics

Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China

^* e-mail: horvathy@univ-tours.fr

Received: 1 September 2009
Revised: 19 October 2009
Published online: 10 December 2009

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 Schrödinger group, which also involves, in addition, Schrödinger 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.