# Anyons in the operational formalism

## Abstract

The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4, 5]. However, this seems to run counter to results in two-dimensional systems, which allow for anyons, particles with statistics which interpolate between Fermi-Dirac and Bose-Einstein (see [6] for a review). In this talk we will show that the results in two dimensions can be made compatible with the operational results. That is, we will show that anyonic behavior is a result of the topology of the space in two dimensions [7], and does not depend on the particles being identical; but that nevertheless, if the particles are identical, the resulting system is still anyonic.

- Authors:

- University at Albany, SUNY (United States)

- Publication Date:

- OSTI Identifier:
- 22390862

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1641; Journal Issue: 1; Conference: MAXENT 2014: Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clos Luce, Amboise (France), 21-26 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANYONS; BOSE-EINSTEIN STATISTICS; BOSONS; FERMI STATISTICS; FERMIONS; QUANTUM MECHANICS; QUANTUM OPERATORS; REVIEWS; SPACE; STATISTICS; TOPOLOGY; TWO-DIMENSIONAL SYSTEMS

### Citation Formats

```
Neori, Klil H., and Goyal, Philip.
```*Anyons in the operational formalism*. United States: N. p., 2015.
Web. doi:10.1063/1.4905978.

```
Neori, Klil H., & Goyal, Philip.
```*Anyons in the operational formalism*. United States. doi:10.1063/1.4905978.

```
Neori, Klil H., and Goyal, Philip. Tue .
"Anyons in the operational formalism". United States.
doi:10.1063/1.4905978.
```

```
@article{osti_22390862,
```

title = {Anyons in the operational formalism},

author = {Neori, Klil H. and Goyal, Philip},

abstractNote = {The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4, 5]. However, this seems to run counter to results in two-dimensional systems, which allow for anyons, particles with statistics which interpolate between Fermi-Dirac and Bose-Einstein (see [6] for a review). In this talk we will show that the results in two dimensions can be made compatible with the operational results. That is, we will show that anyonic behavior is a result of the topology of the space in two dimensions [7], and does not depend on the particles being identical; but that nevertheless, if the particles are identical, the resulting system is still anyonic.},

doi = {10.1063/1.4905978},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1641,

place = {United States},

year = {Tue Jan 13 00:00:00 EST 2015},

month = {Tue Jan 13 00:00:00 EST 2015}

}