Non-relativistic conformal symmetries and Newton-Cartan structures

Apr, 2009
44 pages
Published in:
  • J.Phys.A 42 (2009) 465206
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200920132017202120250510152025
Abstract: (arXiv)
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/qz=2/q, where qq is some rational number. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schr\'odinger Lie algebra, with z=2z=2. For lightlike geodesics, they yield the Conformal Galilean Algebra of Lukierski, Stichel and Zakrzewski, with z=1z=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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