Electromagnetic Excitations of A_n Quantum Hall Droplets

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.