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C. Duval

Publications and source records attributed to C. Duval.

At least 37 records · Page 2Linked to original sources
arXiv2014

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

The Carroll group was originally introduced by Levy-Leblond [1] by considering the limit of the Poincaré group as $c\to0$. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, space-time structure is proposed. A "duality" with the Galilean limit $c\to\infty$ is established. Our theory is illustrated by Carrollian electromagnetism.

gr-qc↗
arXiv2012

Transverse Shifts in Paraxial Spinoptics

The paraxial approximation of a classical spinning photon is shown to yield an "exotic particle" in the plane transverse to the propagation. The previously proposed and observed position shift between media with different refractive indices is modified when the interface is curved, and there also appears a novel, momentum [direction] shift. The laws of thin lenses are modified accordingly.

physics.optics↗
arXiv2008

The geometry of Schrödinger symmetry in non-relativistic CFT

The non-relativistic conformal "Schroedinger" symmetry of some gravity backgrounds proposed recently in the AdS/CFT context, is explained in the "Bargmann framework". The formalism incorporates the Equivalence Principle. Newton-Hooke conformal symmetries, which are analogs of those of Schroedinger in the presence of a negative cosmological constant, are discussed in a similar way. Further examples include topologically massive gravity with negative cosmological constant and the Madelung hydrodynamical description.

hep-th↗
arXiv2006

Fermat Principle for spinning light

Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the ``Optical Hall Effect'' (alias the ``Optical Magnus Effect'') for polarized light.

cond-mat.mes-hall↗
arXiv2006

Strings in plane-fronted gravitational waves

Brinkmann's plane-fronted gravitational waves with parallel rays --~shortly pp-waves~-- are shown to provide, under suitable conditions, exact string vacua at all orders of the sigma-model perturbation expansion.

hep-th↗
arXiv2005

Celestial Mechanics, Conformal Structures, and Gravitational Waves

The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a generalized pp-wave. Bargmann electromagnetism in five dimensions comprises the two Galilean electro-magnetic theories (Le Bellac and Lévy-Leblond). At the quantum level, the $N$-body Schrödinger equation retains the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem: homographic solutions, the virial theorem, Kepler's third law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing 2-tensors, and motions under inverse square law forces with a gravitational constant $G(t)$ varying inversely as time (Dirac). The latter problem is reduced to one with time independent forces for a rescaled position vector and a new time variable; this transformation (Vinti and Lynden-Bell) arises from a conformal transformation preserving the Ricci-flatness (Brinkmann). A Ricci-flat metric representing $N$ non-relativistic gravitational dyons is also pointed out. Our results for general time-dependent $G(t)$ are applicable to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.

hep-th↗
arXiv2005

Berry phase correction to electron density in solids and "exotic" dynamics

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 theorem holds for the symplectic volume form. Suitably defined quantities satisfy hydrodynamic equations.

cond-mat.mes-hall↗
arXiv2005

On Schrödinger superalgebras

We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schrödinger algebra (itself a conformal extension of the Galilei algebra). An `$I$-type' extension exists in any space dimension, and for any pair of integers $N_+$ and $N_-$. It yields an $N=N_++N_-$ superalgebra, which generalizes the N=1 supersymmetry Gauntlett et al. found for a free spin-$\half$ particle, as well as the N=2 supersymmetry of the fermionic oscillator found by Beckers et al. In two space dimensions, new, `exotic' or `$IJ$-type' extensions arise for each pair of integers $ν_+$ and $ν_-$, yielding an $N=2(ν_++ν_-)$ superalgebra of the type discovered recently by Leblanc et al. in non relativistic Chern-Simons theory. For the magnetic monopole the symmetry reduces to $ø(3)\times\osp(1/1)$, and for the magnetic vortex it reduces to $ø(2)\times\osp(1/2)$.

hep-th↗
arXiv2004

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.

hep-th↗
arXiv2004

Anyons with anomalous gyromagnetic ratio & the Hall effect

Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{αβ}S^{αβ}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our model can accommodate any gyromagnetic ratio $g$ and provides us with a novel version of the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes singular when the field takes a critical value, and, for $g\neq2$, the only allowed motions are those which satisfy the Hall law. For each $g\neq2,0$ a secondary Hall effect arises also for another critical value of the field. The non-relativistic limit of our equations yields new models which generalize our previous ``exotic'' model, associated with the two-fold central extension of the planar Galilei group.

hep-th↗
arXiv2003

Chern-Simons vortices

In (2+1) dimensions, the Maxwell term $-(1/4) F_{αβ}F^{αβ}$ can be replaced by the Chern-Simons three-form $(κ/4)ε^{αβγ}A_αF_{βγ}$, yielding a novel type of `electromagnetism'. This has been proposed for studying the Quantum Hall Effect as well as High-Temperature Superconductivity. The gauge field can be coupled to a scalar field either relativistically or non-relativistically. In both cases, one admits finite-energy, vortex solutions.

hep-th↗
arXiv2003

Vanishing of the conformal anomaly for strings in a gravitational wave

Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal anomaly vanishes at the two-loop level. Under some conditions, the anomaly vanishes at all orders.

hep-th↗
arXiv2003

Projectively and conformally invariant star-products

We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp. SO(p+1,q+1))-invariant. We prove the existence of such star-products using the projectively (resp. conformally) equivariant quantization, then prove their uniqueness, and study their main properties. We finally give an explicit formula for the canonical projectively invariant star-product.

math.QA↗
arXiv2002

Spin and exotic Galilean symmetry

A slightly modified and regularized version of the non-relativistic limit of the relativistic anyon model considered by Jackiw and Nair yields particles associated with the twofold central extension of the Galilei group, with independent spin and exotic structure.

hep-th↗
arXiv2001

Exotic galilean symmetry and the Hall effect

The ``Laughlin'' picture of the Fractional Quantum Hall effect can be derived using the ``exotic'' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar magnetic field of critical strength determined by the extension parameters, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.

hep-th↗
arXiv2001

Exotic galilean symmetry in the non-commutative plane, and the Hall effect

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 inverse of the non-commutative parameter, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.

hep-th↗