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Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time

- C. Duval, G. Gibbons, P. Horváthy, P. Zhang
- Physics, Mathematics
- 4 February 2014

The Carroll group was originally introduced by Levy-Leblond (1965 Ann. Inst. Henri Poincare 3 1) by considering the contraction of the Poincare group as c → 0. In this paper an alternative… Expand

108 13- PDF

The exotic Galilei group and the “Peierls substitution”

- C. Duval, P. A. Horv'athy
- Physics, Mathematics
- 28 February 2000

Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not… Expand

226 12- PDF

Non-relativistic conformal symmetries and Newton–Cartan structures

- C. Duval, P. Horváthy
- Mathematics, Physics
- 3 April 2009

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… Expand

222 8- PDF

Conformal Carroll groups and BMS symmetry

- C. Duval, G. Gibbons, P. Horváthy
- Physics, Mathematics
- 24 February 2014

The Bondi–Metzner–Sachs group is shown to be the conformal extension of Levy-Leblond's 'Carroll' group. Further extension to the Newman–Unti group is also discussed in the Carroll framework.

101 8- PDF

Conformally equivariant quantization: existence and uniqueness

- C. Duval, P. Lecomte, V. Ovsienko
- Mathematics
- 4 February 1999

On etablit l'existence et l'unicite d'un calcul symbolique et d'une quantification conformement equivariants sur une variete pseudo-riemannienne conformement plate (M, g), i.e. on met en evidence un… Expand

95 7- PDF

Space of second order linear differential operators as a module over the Lie algebra of vector fields

- C. Duval, V. Ovsienko
- Mathematics, Physics
- 12 September 1994

Abstract The space of linear differential operators on a smooth manifoldMhas a natural one-parameter family of Diff(M)- (and Vect(M)-) module structures, defined by their action on the space of… Expand

48 7

Pukanszky's condition and symplectic induction

- C. Duval, J. Elhadad, G. Tuynman
- Mathematics
- 1992

Pukanszky’s condition is a condition used in obtaining representations from coadjoint orbits. In order to obtain more geometric insight in this condition, we relate it to symplectic induction. It… Expand

33 6- PDF

Conformally equivariant quantization

- C. Duval, V. Ovsienko
- Mathematics
- 27 January 1998

Let $(M,g)$ be a pseudo-Riemannian manifold and $F_\lambda(M)$ the space of densities of degree $\lambda$ on $M$. We study the space $D^2_{\lambda,\mu}(M)$ of second-order differential operators from… Expand

21 6- PDF

Conformal Carroll groups

- C. Duval, G. Gibbons, P. Horváthy
- Mathematics, Physics
- 17 March 2014

Conformal extensions of Levy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k. This… Expand

75 5- PDF

Exotic Galilean symmetry in the non-commutative plane and the Hall effect

- C. Duval, P. A.Horvathy
- Physics
- 12 June 2001

Quantum mechanics in the non-commutative plane is shown to admit the 'exotic' symmetry of the doubly centrally extended Galilei group. When coupled to a planar magnetic field whose strength is the… Expand

163 5- PDF

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