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

arXiv:quant-ph/9710016

The k-fermions as objects interpolating between fermions and bosons

Mohammed Daoud A, Y. Hassouni, M. Kibler

Published Oct 3, 1997• 0 citations
arXivHTMLPDF

Abstract

Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of unity connected to an integer k. The case k=2 corresponds to fermions and the limiting case k going to infinity to bosons. Generalized coherent states and supercoherent states are investigated. The Dirac quantum phase operator and the Fairlie-Fletcher-Zachos algebra are also considered.

DOI
10.48550/arxiv.quant-ph/9710016

Related papers

Generalized supercoherent states

Mohammed Daoud A, M. Kibler, Y. Hassouni

A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.

PAN•Jan 1, 1997•0 citations

On Generalized Super-Coherent States

Mohammed Daoud A, Y. Hassouni, M. Kibler

A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.

arXiv:quant-ph/9804046•Apr 20, 1998•5 citations

CONSTRUCTION OF BOSONS AND FERMIONS OUT OF QUONS

The quon algebra describes particles, “quons, ” that are neither fermions nor bosons, using a label q that parametrizes a smooth interpolation between bosons (q = 1) and fermions (q = −1). Understanding the relation of quons on the one side and bosons or fermions on the other can shed light on the different properties of these two kinds of operators and the statistics which they carry. In particular, local bilinear observables can be constructed from bosons and fermions, but not from quons. In this paper we construct bosons and fermions from quon operators. For bosons, our construction works for −1 ≤ q ≤ 1. The case q = −1 is paradoxical, since that case makes a boson out of fermions, which would seem to be impossible. None the less, when the limit q → −1 is taken from above, the construction works. For fermions, the analogous construction works for −1 ≤ q ≤ 1, which includes the paradoxical case q = 1.

•Jan 1, 2001•0 citations

Quons, an interpolation between bose and fermi oscillators

Oscar Wallace Greenberg

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the statistics of ``quons'' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the $q$-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter $q$ for electrons due to the Ramberg-Snow experiment.

arXiv:cond-mat/9301002•Jan 5, 1993•7 citations

Deformed quons and bi-coherent states

Fabio Bagarello

We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This deformation involves interesting mathematical problems and suggests possible applications to pseudo-hermitian quantum mechanics. We construct bi-coherent states associated to D -pseudo-quons, and we show that they share many of their properties with ordinary coherent states. In particular, we find conditions for these states to exist, to be eigenstates of suitable annihilation operators and to give rise to a resolution of the identity. Two examples are discussed in details, one connected to an unbounded similarity map, and the other to a bounded map.

arXiv:1703.10021•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Apr 1, 2017•26 citations

A Fractional Supersymmetric Oscillator and Its Coherent States

Mohammed Daoud A, M. Kibler

We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and a k-fermion leads to a definition of fractional supercoherent states. Such states involve bosonic coherent states and k-fermionic coherent states. We construct an Hamiltonian which generalizes the ordinary (or Z_2-graded) supersymmetric oscillator Hamiltonian. Our Hamiltonian describes a fractional (or Z_k-graded) supersymmetric oscillator for which the fractional supercoherent states are coherent states.

arXiv:math-ph/9912024•Dec 30, 1999•14 citations
Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of unity connected to an integer k. The case k=2 corresponds to fermions and the limiting case k going to infinity to bosons. Generalized coherent states and supercoherent states are investigated. The Dirac quantum phase operator and the Fairlie-Fletcher-Zachos algebra are also considered.
A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.
A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.
The quon algebra describes particles, “quons, ” that are neither fermions nor bosons, using a label q that parametrizes a smooth interpolation between bosons (q = 1) and fermions (q = −1). Understanding the relation of quons on the one side and bosons or fermions on the other can shed light on the different properties of these two kinds of operators and the statistics which they carry. In particular, local bilinear observables can be constructed from bosons and fermions, but not from quons. In this paper we construct bosons and fermions from quon operators. For bosons, our construction works for −1 ≤ q ≤ 1. The case q = −1 is paradoxical, since that case makes a boson out of fermions, which would seem to be impossible. None the less, when the limit q → −1 is taken from above, the construction works. For fermions, the analogous construction works for −1 ≤ q ≤ 1, which includes the paradoxical case q = 1.
After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the statistics of ``quons'' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the qqq-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter qqq for electrons due to the Ramberg-Snow experiment.
We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This deformation involves interesting mathematical problems and suggests possible applications to pseudo-hermitian quantum mechanics. We construct bi-coherent states associated to D -pseudo-quons, and we show that they share many of their properties with ordinary coherent states. In particular, we find conditions for these states to exist, to be eigenstates of suitable annihilation operators and to give rise to a resolution of the identity. Two examples are discussed in details, one connected to an unbounded similarity map, and the other to a bounded map.
We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and a k-fermion leads to a definition of fractional supercoherent states. Such states involve bosonic coherent states and k-fermionic coherent states. We construct an Hamiltonian which generalizes the ordinary (or Z_2-graded) supersymmetric oscillator Hamiltonian. Our Hamiltonian describes a fractional (or Z_k-graded) supersymmetric oscillator for which the fractional supercoherent states are coherent states.