相关论文: Exotic galilean symmetry, non-commutativity & the …
The ``exotic'' particle model with non-commuting position coordinates, associated with the two-parameter central extension of the planar Galilei group, can be used to derive the ground states of the Fractional Quantum Hall Effect. The…
Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized…
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…
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,…
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic'' central extension is introduced. It is used to describe non-relativistic anyons coupled to an electromagnetic field. Our…
Laughlin's Ansatz to explain the fractional Quantum Hall effect is derived by coupling a particle associated with ``exotic'' the two-fold central extension of the planar Galilei group. The reduced system is identical to the one used to…
When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting boosts, but also the two-fold centrally…
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 commute. Our model can be viewed as the…
The non-relativistic version of the non commutative Field Theory, recently introduced by Lozano, Moreno and Schaposnik [1], is shown to admit the ``exotic'' Galilean symmetry found before for point particles.
The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and…
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…
We review the fermionic Chern-Simons field theory for the Fractional Quantum Hall Effect (FQHE). We show that in this field theoretic approach to the problem of interacting electrons moving in a plane in the presence of an external magnetic…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We present a different approach to the fractional quantum Hall effect (FQHE), focusing it as a consequence of the change in the symmetry of the Hamiltonian of every electron in a two-dimensional electron gas (2DEG) under the application of…
We show that the Lukierski et al. model, invariant with respect to the two-fold centrally extended Galilei group, can be decomposed into an infinite number of independent copies (differing in their spin) of the ``exotic'' particle of Duval…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
$N$ "exotic" [alias non-commutative] particles with masses $m_a$, charges $e_a$ and non-commutative parameters $\theta_a$, moving in a uniform magnetic field $B$, separate into center-of-mass and internal motions if Kohn's condition…
We study some aspects of recent proposals to use the noncommutative Chern-Simons theory as an effective description of some planar condensed matter models in strong magnetic fields, such as the Quantum Hall Effect. We present an alternative…
We clearly show that the symplectic structures deformations lead, upon quantization, to quantum theories of non commutative fields. Two variants of deformations are considered. The quantization is performed and the modes expansions of the…
The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in…