Anyons in the operational formalism
Abstract
The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically wellmotivated 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 socalled Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4, 5]. However, this seems to run counter to results in twodimensional systems, which allow for anyons, particles with statistics which interpolate between FermiDirac and BoseEinstein (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), 2126 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; BOSEEINSTEIN STATISTICS; BOSONS; FERMI STATISTICS; FERMIONS; QUANTUM MECHANICS; QUANTUM OPERATORS; REVIEWS; SPACE; STATISTICS; TOPOLOGY; TWODIMENSIONAL 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. 2015.
"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 wellmotivated 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 socalled Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4, 5]. However, this seems to run counter to results in twodimensional systems, which allow for anyons, particles with statistics which interpolate between FermiDirac and BoseEinstein (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 = 2015,
month = 1
}

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