Electromagnetic Excitations of Aₙ Quantum Hall Droplets

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The classical description of Aₙ 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 Aₙ statistics, living in the complex projective space CPᵏ with U(1)background magnetic field. We explicitly calculate the bulk and edge actions. Some particular symplectic deformations are also considered.