Phase Space Reduction and Vortex Statistics: An Anyon Quantization Ambiguity

TL;DR

This paper investigates the quantization of two charged vortices in a Ginzburg-Landau model related to the fractional quantum Hall effect, revealing that different quantization methods are inequivalent unless vortices follow conventional statistics.

Contribution

It compares two quantization approaches for vortex dynamics and shows their inequivalence under fractional statistics, clarifying the role of vortex statistics in phase space reduction.

Findings

Different quantization methods are inequivalent for fractional vortices.

Conventional statistics (fermionic/bosonic) restore equivalence.

Implications for vortex quantization in quantum Hall systems.

Abstract

We examine the quantization of the motion of two charged vortices in a Ginzburg--Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of implementing the constraints are inequivalent unless the vortices are quantized with conventional statistics; either fermionic or bosonic.