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Title: 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:
;  [1]
  1. 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}
}