Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes

Christian Duval (1, 2) , Peter Horvathy (3)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332
3 LMPT - Laboratoire de Mathématiques et Physique Théorique

Finite-dimensional nonrelativistic conformal Lie algebras spanned by polynomial vector fields of Galilei spacetime arise if the dynamical exponent is z=2/N with N=1,2,\dots. Their underlying group structure and matrix representation are constructed (up to a covering) by means of the Veronese map of degree N. Suitable quotients of the conformal Galilei groups provide us with Newton-Hooke nonrelativistic spacetimes with a quantized reduced negative cosmological constant \lambda=-N.

Mots clés: Schrödinger algebra; conformal Galilei algebras and Galilei groups; Newton-Cartan theory; Veronese maps; Newton-Hooke spacetimes; cosmological constant

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Christian Duval, Peter Horvathy. Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes. Journal of Physics A: Mathematical and Theoretical, 2011, 44, 335203 (21pp). ⟨10.1088/1751-8113/44/33/335203⟩. ⟨hal-00583704v3⟩