Conformal Anisotropic Mechanics

TL;DR

This paper introduces a classical mechanics model with anisotropic scale transformations, generalizing conformal mechanics, and explores its symmetries, thermodynamics, and relation to gravity at Lifshitz points.

Contribution

It develops a classical mechanics framework incorporating anisotropic scaling, extending conformal mechanics, and derives associated symmetries and thermodynamic properties.

Findings

Model consistent with gravity dispersion relations at Lifshitz points

Constructed dynamical symmetries for arbitrary z

Derived Boltzmann distribution compatible with anisotropic scaling

Abstract

In this paper we implement scale anisotropic transformations in the space-time in classical mechanics. The resulting system is consistent with the dispersion relation of gravity at a Lifshitz point recently considered in arXiv:0901.3775. 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 arXiv:0907.4755.