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arXiv · hep-th/9207093

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

Theodore J. Allen
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Abstract

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 Schrödinger 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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Theodore J. Allen. 1992-07-28. Collective Coordinate Action for Charged Sigma-Model Vortices in Finite Geometries. https://doi.org/10.1142/s0217732393001537

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