Effective Wess–Zumino–Witten action for edge states of quantum Hall systems on Bergman ball Original Research Article

Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball image. This can be done by considering a system of particles living on image in the presence of an uniform magnetic field B and realizing the ball as the coset space image. In quantizing the theory on image, we define the wavefunctions as the Wigner image-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 image 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.