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

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

1 CPT - Centre de Physique Théorique - UMR 6207
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 \emph{conformal Galilei groups} provide us with Newton-Hooke nonrelativistic spacetimes with quantized negative cosmological constant $\Lambda=-Nd$, where $d$ the dimension of space

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. 2011. ⟨hal-00583704v1⟩