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

- C. Duval, G. Gibbons, P. Horvathy, P. M. Zhang
- Mathematics
- 4 February 2014

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

Conformal Carroll groups and BMS symmetry

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

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

The exotic Galilei group and the “Peierls substitution”

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

Non-relativistic conformal symmetries and Newton–Cartan structures

- C. Duval, P. Horvathy
- 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

Time-dependent quantum systems and chronoprojective geometry

Chronoprojective transformations in the framework of five-dimensional Schrödinger formalism are used to construct the solution of the Schrödinger equation with a time-dependent harmonic potential… Expand

Conformal Carroll groups

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

Conformal extensions of Lévy–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

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

Pukanszky's condition and symplectic induction

- C. Duval, J. Elhadad, G. Tuynman
- Physics, 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

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

Berry Phase Correction to Electron Density in Solids and

- C. Duval, Z. Horváth, P. Horvathy, L. Martina, P. Stichel
- Physics
- 2 June 2005

Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for ``exotic'' Galilean dynamics. The system is indeed Hamiltonian and Liouville's… Expand

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