29 Citations
Matrix model for a quantum Hall droplet with manifest particle-hole symmetry
- Physics
- 2005
We find that a gauged matrix model of rectangular fermionic matrices (a matrix version of the fermion harmonic oscillator) realizes a quantum hall droplet with manifest particle-hole symmetry. The…
Electromagnetic Excitations of Hall Systems on Four-Dimensional Space
- Physics
- 2011
The noncommutativity of a four-dimensional phase space is introduced from a purely symplectic point of view. We show that there is always a coordinate map to locally eliminate the gauge fluctuations…
Symplectic fluctuations for electromagnetic excitations of Hall droplets
- Physics
- 2010
We show that the integer quantum Hall effect systems in a plane, sphere or disc can be formulated in terms of an algebraic unified scheme. This can be achieved by making use of a generalized…
Electromagnetic Excitations of A_n Quantum Hall Droplets
- Physics
- 2010
The classical description of A_n internal degrees of freedom is given by making use of the Fock--Bargmann analytical realization. The symplectic deformation of phase space, including the internal…
Quantum Hall Effect, Bosonization and Chiral Actions in Higher Dimensions
- Physics
- 2010
We give a brief review of the Quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional…
Geometry of the quantum Hall effect: An effective action for all dimensions
- Physics
- 2016
We present a general formula for the topological part of the effective action for integer quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around…
Noncommutative scalar fields from symplectic deformation
- Mathematics
- 2008
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space-time. It is shown that the noncommutativity originates from the the deformation of symplectic…
References
SHOWING 1-10 OF 58 REFERENCES
Quantum Hall states as matrix Chern-Simons theory
- Physics
- 2001
We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the…
Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
- Physics
- 2001
We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard…
Collective excitations at the boundary of a four-dimensional quantum Hall droplet
- Physics
- 2001
In this work we investigate collective excitations at the boundary of a recently constructed four-dimensional (4D) quantum Hall state. Local bosonic operators for creating these collective…
Matrix models of 4-dimensional quantum Hall fluids
- Physics
- 2002
We propose two non-abelian Chern-Simons matrix models as the effective descriptions of 4-dimensional quantum Hall fluids. One of them describes a new type of 4-dimensional quantum Hall fluid on the…
Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid
- Physics
- 2002
We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment…