Non-relativistic conformal symmetries and Newton-Cartan structures

Details Non-relativistic conformal symmetries and Newton-Cartan structures Non-relativistic conformal symmetries and Newton-Cartan structures

2009-04-03

arxiv.org/abs/0904.0531v5

J.Phys.A42:465206,2009

Physics

Mathematical Physics

LaTeX, 47 pages. Bibliographical improvements. To appear in J. Phys. A

Scientific paper

10.1088/1751-8113/42/46/465206

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational "dynamical exponent", $z$. The Schr\"odinger-Virasoro algebra of Henkel et al. corresponds to $z=2$. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schr\"odinger Lie algebra, for which z=2. For lightlike geodesics, they yield, in turn, the Conformal Galilean Algebra (CGA) and Lukierski, Stichel and Zakrzewski [alias "$\alt$" of Henkel], with $z=1$. Physical systems realizing these symmetries include, e.g., classical systems of massive, and massless non-relativistic particles, and also hydrodynamics, as well as Galilean electromagnetism.

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