# Phase space reduction and vortex statistics: An anyon quantization ambiguity

## 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.

- Authors:

- (Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States))

- Publication Date:

- OSTI Identifier:
- 7239189

- DOE Contract Number:
- AC02-76ER00881

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review, D (Particles Fields); (United States); Journal Volume: 49:12

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GINZBURG-LANDAU THEORY; VORTICES; QUANTIZATION; PHASE SPACE; STATISTICS; MATHEMATICAL SPACE; MATHEMATICS; SPACE; 661100* - Classical & Quantum Mechanics- (1992-); 661300 - Other Aspects of Physical Science- (1992-)

### Citation Formats

```
Allen, T.J., Bordner, A.J., and Crossley, D.B.
```*Phase space reduction and vortex statistics: An anyon quantization ambiguity*. United States: N. p., 1994.
Web. doi:10.1103/PhysRevD.49.6907.

```
Allen, T.J., Bordner, A.J., & Crossley, D.B.
```*Phase space reduction and vortex statistics: An anyon quantization ambiguity*. United States. doi:10.1103/PhysRevD.49.6907.

```
Allen, T.J., Bordner, A.J., and Crossley, D.B. Wed .
"Phase space reduction and vortex statistics: An anyon quantization ambiguity". United States.
doi:10.1103/PhysRevD.49.6907.
```

```
@article{osti_7239189,
```

title = {Phase space reduction and vortex statistics: An anyon quantization ambiguity},

author = {Allen, T.J. and Bordner, A.J. and Crossley, D.B.},

abstractNote = {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.},

doi = {10.1103/PhysRevD.49.6907},

journal = {Physical Review, D (Particles Fields); (United States)},

number = ,

volume = 49:12,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 1994},

month = {Wed Jun 15 00:00:00 EDT 1994}

}

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