Electromagnetic Excitations of A_n Quantum Hall Droplets

Abstract

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.

24 pages

References in corpus (9)

• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball
• Quantum Hall Effect on the Flag Manifold F_2
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory
• Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States
• Representations and Properties of Generalized $A_r$ Statistics, Coherent States and Robertson Uncertainty Relations
• A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras
• Chiral bosons on Bargmann space associated with A${}_r$ Statistics