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Full 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.
Contents
Introduction.- Bosons and Pseudo-Bosons.- Other Ladder Operators.- Our Way to the BCH Formula.- Bi-coherent States.- Examples of Bi-coherent States.- Weak Pseudo-Bosons and Related Bi-coherent States.- An Application to Transition Probability.- Conclusions.- Appendix.
