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:1207.2013 · Journal of Physics A Mathematical and Theoretical

(Regular) pseudo-bosons versus bosons

Fabio Bagarello

Published Dec 6, 2010• 25 citations
arXivHTMLPDF

Abstract

We discuss in which sense the so-called regular pseudo-bosons, recently introduced by Trifonov and analyzed in some detail by the author, are related to ordinary bosons. We repeat the same analysis for pseudo-bosons , and analyze the role played by certain intertwining operators, which may be bounded or not.
DOI
10.1088/1751-8113/44/1/015205

Related papers

Pseudo-bosons, so far

Fabio Bagarello

In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called pseudo-bosons. They arise from a special deformation of the canonical commutation relation [a,a †]= ll, which is replaced by [a,b]=ll, with b not necessarily equal to a †. We start discussing some of their mathematical properties and then we discuss several examples.

•Jan 1, 2011•24 citations

Bi-squeezed states arising from pseudo-bosons

F Bagarello, F Gargano, S Spagnolo

Abstract Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the bi-squeezed states , and we deduce their main mathematical properties. We relate bi-squeezed states to the so-called regular and non regular pseudo-bosons. We show that these two cases are different, from a mathematical point of view. Some physical examples are considered.

arXiv:1809.05346•Journal of Physics A Mathematical and Theoretical•Sep 14, 2018•15 citations

Nonlinear pseudo-bosons versus hidden Hermiticity

Fabio Bagarello, Miloslav Znojil

The increasingly popular concept of a ‘hidden’ Hermiticity of operators is compared with the recently introduced notion of nonlinear pseudo-bosons . The formal equivalence between these two notions is deduced under very general assumptions. Examples of their applicability in quantum mechanics are discussed.

arXiv:1109.0605•Journal of Physics A Mathematical and Theoretical•Sep 23, 2011•21 citations

Nonlinear pseudo-bosons versus hidden Hermiticity: II. The case of unbounded operators

Fabio Bagarello, Miloslav Znojil

A close parallelism between the notions of nonlinear pseudobosons and those of an apparent non-Hermiticity of observables as shown in part I (2011 J. Phys. A: Math. Theor. 44 415305) is demonstrated to survive the transition to the quantum models using an unbounded metric in the so-called standard Hilbert space of states.

arXiv:1202.2028•Journal of Physics A Mathematical and Theoretical•Mar 2, 2012•24 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 position dependent mass Hamiltonian and abstract ladder operators

Fabio Bagarello, Emanuele Balistreri, Antonino Faddetta

We consider the Hamiltonian $H$ of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators}, in the attempt to find its eigenvalues and eigenvectors. We don't assume that $H$ is self-adjoint, while we focus on the case of a factorizable operator. We show then that pseudo-bosonic operators play a relevant role in this analysis, and we construct bi-coherent states attached to these operators. Explicit examples are discussed.

math-phCross-listedarXiv:2605.01443•May 5, 2026•0 citations
In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called pseudo-bosons. They arise from a special deformation of the canonical commutation relation [a,a †]= ll, which is replaced by [a,b]=ll, with b not necessarily equal to a †. We start discussing some of their mathematical properties and then we discuss several examples.
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 consider the Hamiltonian HHH of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators}, in the attempt to find its eigenvalues and eigenvectors. We don't assume that HHH is self-adjoint, while we focus on the case of a factorizable operator. We show then that pseudo-bosonic operators play a relevant role in this analysis, and we construct bi-coherent states attached to these operators. Explicit examples are discussed.