# Two Approaches to Fractional Statistics in the Quantum Hall Effect: Idealizations and the Curious Case of the Anyon

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## Abstract

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects—(what we may call) the *topological approach *to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative *geometric approach* is outlined and endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed.

## Keywords

Idealization Approximation Emergence Reduction Aharonov–Bohm effect Quantum Hall effect Anyons Fractional Statistics Representation Explanation## Notes

### Acknowledgments

Parts of this paper were presented at the “Bucharest Colloquium in Analytic Philosophy: New Directions in the Philosophy of Physics” conference at University of Bucharest. I am grateful to the audience for stimulating discussion, to Iulian Toader for editing this volume of *Foundations of Physics*, and to two anonymous referees for helpful comments. I am especially grateful to John Earman and John D. Norton for comments on earlier versions of this paper, numerous insightful discussions, and their constant support. This paper is heavily in debt to work done by John Earman, who initially drew my attention to the main issues discussed in this paper, and has been especially kind in helping me work through the finer details. Special thanks to Naharin Shech for her help with figures.

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