On the NCCS model of the quantum Hall fluid

Details On the NCCS model of the quantum Hall fluid On the NCCS model of the quantum Hall fluid

2006-06-30

arxiv.org/abs/hep-th/0606286v2

Eur.Phys.J.C50:1013-1017,2007

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, no figures, minor corrections, accepted in Eur. Phys. J. C

Scientific paper

10.1140/epjc/s10052-007-0265-z

Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the $\nu=1$ integer quantum Hall effect (IQHE) state on the fractional quantum Hall effect (FQHE) $\nu=\frac{1}{2p+1}$ 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 reconstructed. It is demonstrated that the geometric transformations induce quantum-mechanical non-unitary similarity transformations, establishing the interplay between integral and fractional QHEs.

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