Pseudo-bosons, so far

Abstract

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 {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^{†}$. We start discussing some of their mathematical properties and then we discuss several examples.

In press in Reports on Mathematical Physics

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Examples of Pseudo-bosons in quantum mechanics
• Construction of pseudo-bosons systems
• Mathematical aspects of intertwining operators: the role of Riesz bases
• Intertwining operators between different Hilbert spaces: connection with frames
• Vector coherent states and intertwining operators
• Two-parameters pseudo-bosons

Cited by in corpus (11)

• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
• Linear Pseudo-fermions
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• Non-self-adjoint hamiltonians defined by Riesz bases
• More mathematics for pseudo-bosons
• $\mathcal{D}$ pseudo-bosons in quantum models
• Damping and Pseudo-fermions
• Weak commutation relations of unbounded operators: nonlinear extensions
• Abstract ladder operators and their applications
• Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics