Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-30
Int.J.Geom.Meth.Mod.Phys.4:1187-1204,2007
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, clarifications and misprints corrected, version published in IJGMMP
Scientific paper
10.1142/S0219887807002508
We 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.
Daoud Mohammed
Jellal Ahmed
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