# On the NCCS model of the quantum Hall fluid

@article{Eliashvili2007OnTN, title={On the NCCS model of the quantum Hall fluid}, author={Merab Eliashvili and George Tsitsishvili}, journal={The European Physical Journal C}, year={2007}, volume={50}, pages={1013-1017} }

Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the ν=1 integer quantum Hall effect (IQHE) state on the $\nu=\frac{1}{2p+1}$ fractional quantum Hall effect (FQHE) states. Using the hydrodynamical description of the quantum Hall fluid, it is shown that these transformations are generated by vector fields satisfying the Gauss law in the interacting non-commutative Chern–Simons gauge theory, and the corresponding field-theory Lagrangian is… Expand

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#### References

SHOWING 1-10 OF 13 REFERENCES

The Quantum Hall Fluid and Non-Commutative Chern Simons Theory

- Physics
- 2001

The first part of this paper is a review of the author's work with S. Bahcall which gave an elementary derivation of the Chern Simons description of the Quantum Hall effect for filling fraction… Expand

Area preserving transformationsin non-commutative space and NCCS theory

- Mathematics, Physics
- 2003

Abstract.We propose a heuristic rule for the area transformation on the non-commutative plane. The non-commutative area preserving transformations are quantum deformations of the classical symplectic… Expand

"Topological" (Chern-Simons) quantum mechanics.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1990

Two quantum-mechanical models are constructed that are analogs of three-dimensional, topologically massive as well as Chern-Simons gauge-field theories, and the phase-space reductive limiting procedure that takes the former to the latter is studied. Expand

CHERN–SIMONS THEORY AND QUANTUM FIELDS IN THE LOWEST LANDAU LEVEL

- Physics
- 2000

By considering the area preserving geometric transformations in the configuration space of electrons moving in the lowest Landau level (LLL) we arrive at the Chern–Simons type Lagrangian. Imposing… Expand

Composite-fermion approach for the fractional quantum Hall effect.

- Physics, Medicine
- Physical review letters
- 1989

It is proposed that the fractional quantum Hall effect of electrons can be physically understood as a manifestation of the integer quantumHall effect of composite fermionic objects consisting of electrons bound to an even number of flux quanta. Expand

Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations

- Physics
- 1983

This Letter presents variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.

Eur. Phys. J. C

- Eur. Phys. J. C
- 2003

Int. J. Mod. Phys. B

- Int. J. Mod. Phys. B
- 2000

On the geometric formulation of the Chern– Simons theory of quantum Hall effect

- Proc. Second Int. Meeting " Mathematical Methods in Modern Theoretical Physics
- 1999

Phys. Rev. D

- Phys. Rev. D
- 1990