Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

ANYON WAVE FUNCTIONS FROM ANYON FIELD OPERATORS

P. A. Marchetti

Published Jun 1, 1992• 6 citations
Publisher

Abstract

We consider a Quantum Field Theory in two space dimensions exhibiting anyon particle excitations and we show how one can derive the structure of wave functions for anyons from the commutation properties of the anyon field operators.
DOI
10.1142/s0217979292001146

Related papers

A Short Guide to Anyons and Modular Functors

Simon Burton

To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to combine anyons, $F^{abc}_{d}$ to re-associate such combinations, and $R^{ab}_c$ to commute or braid these anyons. Although there is a powerful string-diagram notation that greatly assists these manipulations, we still appear to be operating on particles arranged on a one-dimensional line, algebraically ordered from left to right. The obvious question is, where is the other dimension? The topological framework for considering these anyons as truly living in a two dimensional space is known as a modular functor, or topological quantum field theory. In this work we show how the apparently one-dimensional algebraic anyon theory is secretly the theory of anyons living in a fully two-dimensional system. The mathematical literature covering this secret is vast, and we try to distill this down into something more manageable.

arXiv:1610.05384•Oct 17, 2016•4 citations

The basic theoretical formalism of anyon in quantum mechanics

Ren-Gui Zhu

The concept of anyons is introduced through discussing the origin of the exchange symmetry of wave functions and the commutation relations of field operators.Moreover,a rigorous proof of the commutation relations of one-dimensional anyonic field operators is presented in detail.The content of this paper is a helpful supplement to the common teaching course of quantum mechanics.

College Physics•Jan 1, 2010•0 citations

Thermal correlators of anyons in two dimensions

N Ilieva, H Narnhofer, W Thirring

The anyon fields have a trivial α-commutator for α not integer. For integer α the commutators become temperature-dependent operator-valued distributions. The n -point functions do not factorize as for quasifree states.

arXiv:math-ph/0004006•Journal of Physics A Mathematical and General•Mar 30, 2001•1 citation

Anyons in the operational formalism

Klil H. Neori, Philip Goyal

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.

arXiv:1410.8080•AIP conference proceedings•Jan 1, 2015•0 citations

Anyons in the Operational Formalism

Klil H. Neori, Philip Goyal

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.

•Aug 14, 2016•1 citation

Relativistic Wave Equation for Anyons

V. P. Nair

I describe how, starting from fundamental symmetry principles, a relativistic theory of anyons can be formulated.

International Journal of Modern Physics B•Jun 1, 1991•4 citations
To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as ⊗\otimes⊗ to combine anyons, FdabcF^{abc}_{d}Fdabc​ to re-associate such combinations, and RcabR^{ab}_cRcab​ to commute or braid these anyons. Although there is a powerful string-diagram notation that greatly assists these manipulations, we still appear to be operating on particles arranged on a one-dimensional line, algebraically ordered from left to right. The obvious question is, where is the other dimension? The topological framework for considering these anyons as truly living in a two dimensional space is known as a modular functor, or topological quantum field theory. In this work we show how the apparently one-dimensional algebraic anyon theory is secretly the theory of anyons living in a fully two-dimensional system. The mathematical literature covering this secret is vast, and we try to distill this down into something more manageable.
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.
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.