2006/05/31 by Mohammed Daoud, MOHAMMED DAOUD, Ahmed Jellal +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Spectral Theory in Mathematical Physics #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1142/s0219887807002508
published as Int.J.Geom.Meth.Mod.Phys.4:1187-1204,2007 · 18 pages, clarifications and misprints corrected, version published in IJGMMP
openalex publication_date 2007/11/01 · arxiv created 2008/05/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We algebraically analyze the quantum Hall effect of a system of particles living on the disc B 1 in the presence of a 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 [Formula: see text]-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.