Non-relativistic conformal symmetries and Newton-Cartan structures

Abstract : This article provides us with a unifying clas\-sification of the conformal infini\-tesimal sym\-metries 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 ``dyna\-mical exponent'', $z$. The Schrödinger-Virasoro algebra of Henkel et al. corresponds to $z=2$. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schrödinger 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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Submitted on : Saturday, September 26, 2009 - 5:43:25 PM
Last modification on : Wednesday, March 21, 2018 - 10:54:03 AM
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  • HAL Id : hal-00373011, version 5
  • ARXIV : 0904.0531

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Christian Duval, Péter A. Horvathy. Non-relativistic conformal symmetries and Newton-Cartan structures. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42, pp.465206. ⟨hal-00373011v5⟩

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