Electromagnetic Excitations of Hall Systems on Four Dimensional Space

Details Electromagnetic Excitations of Hall Systems on Four Dimensional Space Electromagnetic Excitations of Hall Systems on Four Dimensional Space

2011-03-21

arxiv.org/abs/1103.3920v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages. Version to appear in IJGMMP (2011)

Scientific paper

The noncommutativity of a four-dimensional phase space is introduced from a purely symplectic point of view. We show that there is always a coordinate map to locally eliminate the gauge fluctuations inducing the deformation of the symplectic structure. This uses the Moser's lemma; a refined version of the celebrated Darboux theorem. We discuss the relation between the coordinates change arising from Moser's lemma and the Seiberg--Witten map. As illustration, we consider the quantum Hall systems on CP^2. We derive the action describing the electromagnetic interaction of Hall droplets. In particular, we show that the velocities of the edge field, along the droplet boundary, are noncommutativity parameters-dependents.

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