Collective Coordinate Action for Charged Sigma-Model Vortices in Finite Geometries

Details Collective Coordinate Action for Charged Sigma-Model Vortices in Finite Geometries Collective Coordinate Action for Charged Sigma-Model Vortices in Finite Geometries

1992-07-28

arxiv.org/abs/hep-th/9207093v2

Mod.Phys.Lett. A8 (1993) 1815-1820

Physics

High Energy Physics

High Energy Physics - Theory

7 pp., Plain TeX (macros included), MAD/TH-92-03

Scientific paper

10.1142/S0217732393001537

In this Letter the method of Lund is applied to formulate a variational principle for the motion of charged vortices in an effective non-linear Schr\"{o}dinger field theory describing finite size two-dimensional quantum Hall samples under the influence of an arbitrary perpendicular magnetic field. Freezing out variations in the modulus of the effective field yields a $U(1)$ sigma-model. A duality transformation on the sigma-model reduces the problem to finding the Green function for a related electrostatics problem. This duality illuminates the plasma analogy to the Laughlin wave function.

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