Pseudo-Bosons and Their Coherent States

Beschreibung

This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.
This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.
Discusses in detail all delicate mathematical aspects related to the analysis of canonical commutation relations Gives an in-depth clarification of the Baker-Campbell-Hausdoff formula Presents recent developments and new results on non self-adjoint operators

Autor*in

Fabio Bagarello

Themen in »Pseudo-Bosons and Their Coherent States«

bi-coherent states biorthogonal families of vectors deformed canonical commutation relations transition probabilities for non self-adjoint Hamiltonians dynamics for non self-adjoint Hamiltonians distributions in quantum mechanics eigenvectors and eigenvalues for non self-adjoint Hamiltonians pseudo-fermions truncated pseudo-bosons

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“The content of the book is clearly presented. It brings together many interesting and useful developments in relation to non-selfadjoint operators and the generalization of coherent states as related to pseudo-bosonic calculus.” (Jean-Pierre Gazeau, Mathematical Reviews, March, 2023)
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