Non-relativistic conformal symmetries and Newton-Cartan structures
Résumé
Non-relativistic conformal infinitesimal transformations are derived directly from the structure of Galilei spacetime. They form, as originally found by Henkel et al., an infinite dimensional Virasoro-like Lie algebra. Its finite-dimensional subalgebras are labeled by the "dynamical exponent" $z=2/q$, where $q$ is some rational number. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schrödinger Lie algebra, with $z=2$. For lightlike geodesics, they yield the Conformal Galilean Algebra of Lukierski, Stichel and Zakrzewski, with $z=1$. The purpose of the present article is to provide a unifying classification of the various conformal infinitesimal symmetries of Newton-Cartan spacetime. Physical systems which realize these symmetries include, e.g., classical systems of massive and massless non-relativistic particles.
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