ELECTROMAGNETIC EXCITATIONS OF A n QUANTUM HALL DROPLETS (original) (raw)

2010, International Journal of Modern Physics A

The classical description of A n internal degrees of freedom is given by making use of the Fock-Bargmann analytical realization. The symplectic deformation of phase space, including the internal degrees of freedom, is discussed. We show that the Moser's lemma provides a mapping to eliminate the fluctuations of the symplectic structure, which become encoded in the Hamiltonian of the system. We discuss the relation between Moser and Seiberg-Witten maps. One physics applications of this result is the electromagnetic excitation of a large collection of particles, obeying the generalized A n statistics, living in the complex projective space CP k with U (1) background magnetic field. We explicitly calculate the bulk and edge actions. Some particular symplectic deformations are also considered. Quantum Hall effect in higher dimensions has intensively been investigated in the last decade from different point of views . This yielded interesting results such as the bosonization [2, 11-13] that has been achieved by making use of the incompressible Hall droplet picture. In this framework, the edge excitations of a quantum Hall droplet are described by a generalized Wess-Zumino-Witten action. Recently, the electromagnetic excitations of a quantum Hall droplet was discussed by Karabali [11] and Nair for the Landau systems in the complex projective space CP k . In fact, the corresponding bulk and edge actions were derived . Interestingly, it was shown that the bulk contribution coincides with the (2k + 1)-dimensional Chern-Simons action .