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.

Auteur

Fabio Bagarello graduated in Physics at the University of Palermo in 1987 and, then, he received the PhD in High Energy Physics from SISSA, Trieste, in 1991. Since 2010, he is full professor in Mathematical Physics at the University of Palermo. He was Distinguished Professor at Cape Town University in 2017, and is a member of the Weyl Prize Selection Committee. He collaborates with many scientists in Canada, Japan, U.K., Sweden, and France. His research focusses on modeling complex systems and on quantum mechanical systems with a dynamic driven by non self-adjoint Hamiltonians. He wrote two monographs on the first topic and edited two books on the second one. He also organized international conferences in Marseille, Paris, and Palermo, on the topics related to his scientific work.

Contenu

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.