Conformal anisotropic mechanics

Abstract

In this paper we implement scale anisotropic transformations in the space-time in classical me chanics. The resulting system is consistent with the dispersion relation of gravity at a Lifshitz point recently considered in [9]. Also, we show that our model is a generalization of the conformal mechanics of Alfaro, Fubini and Furlan. For arbitrary z we construct the dynamical symmetries that correspond to the Schroedinger algebra. Furthermore, we obtain the Boltzman distribution for a gas of free particles compatible with anisotropic scaling transformations and compare our result with the corresponding thermodynamics of the recent anisotropic black branes proposed in PACS numbers : Valid PACS appear here