Pseudo-bosons and their coherent states. (English) Zbl 1510.81083
Mathematical Physics Studies. Cham: Springer (ISBN 978-3-030-94998-3/hbk; 978-3-030-94999-0/ebook). xi, 201 p. (2022).
Publisher’s description: 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.
MSC:
81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
14D15 | Formal methods and deformations in algebraic geometry |
81Q12 | Nonselfadjoint operator theory in quantum theory including creation and destruction operators |
81S40 | Path integrals in quantum mechanics |
81R30 | Coherent states |
46N50 | Applications of functional analysis in quantum physics |
81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |