Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-30
Nucl.Phys.B764:109-127,2007
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, clarifications and some equations removed, version published in NPB
Scientific paper
10.1016/j.nuclphysb.2006.11.032
Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball {\bf B}^k. This can be done by considering a system of particles living on {\bf B}^k 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 {\bf{B}}^k, we define the wavefunctions as the Wigner \cal{D}-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.
Daoud Mohammed
Jellal Ahmed
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