Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States

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dc.creatorDaoud, Mohammed
dc.creatorJellal, Ahmed
dc.date2006-05-30
dc.date2008-05-06
dc.date.accessioned2026-07-07T11:06:35Z
dc.date.available2026-07-07T11:06:35Z
dc.descriptionWe algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess-Zumino-Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.
dc.description18 pages, clarifications and misprints corrected, version published in IJGMMP
dc.identifierhttps://arxiv.org/abs/hep-th/0605290
dc.identifierhttp://arxiv.org/abs/hep-th/0605290
dc.identifierInt.J.Geom.Meth.Mod.Phys.4:1187-1204,2007
dc.identifierdoi:10.1142/S0219887807002508
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189566
dc.subjectHigh Energy Physics - Theory
dc.subjectMesoscale and Nanoscale Physics
dc.titleQuantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States
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