2006/05/31 by Mohammed Daoud, M. Daoud, Ahmed Jellal · 1 citation
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2006.11.032
published as Nucl.Phys.B764:109-127,2007 · 19 pages, clarifications and some equations removed, version published in NPB
openalex publication_date 2007/01/02 · arxiv created 2007/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball \bf Bk. This can be done by considering a system of particles living on \bf Bk in the presence of an uniform magnetic field B and realizing the ball as the coset space SU(k,1)/U(k). In quantizing the theory on \bfBk, we define the wavefunctions as the Wigner \calD-functions satisfying a set of suitable constraints. The corresponding Hamiltonian is mapped in terms of the right translation generators. In the lowest Landau level, we obtain the wavefunctions as the SU(k,1) coherent states. This are used to define the star product, density matrix and excitation potential in higher dimensions. With these ingredients, we construct a generalized effective Wess-Zumino-Witten action for the edge states and discuss their nature.