Non-relativistic conformal symmetries and Newton–Cartan structures

By C. Duval, P. Horváthy. 2009

283 citations recorded by the source corpus.

This paper 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 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) of Lukierski, Stichel and Zakrzewski (alias ‘’ 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.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/cc1e5a43b98f28c62274972f78ace9e01a858144

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time (2014, methodology): “Let us now present a general geometric definition of Carroll manifolds and transformations which makes no mention of the Poincaré, group and its contractions but rather is dual to that of NewtonCartan manifolds [24, 25].”
Newtonian gravity and the Bargmann algebra (2010, background): “es corresponding tothe time and the radial directions [10]. This leads to a foliation where the time direction is replaced by a two-dimensional 4For other aspects of Newton-Cartan gravity, see, e.g., [13, 14] 16 AdS 2 space. This requires a contraction of the Poincar´e algebra in which the Bargmann ”
On the coupling of Galilean-invariant field theories to curved spacetime (2014, methodology): “In this case the Newton-Cartan structure is called a Newton-Cartan-Milne structure [14].”