Pseudo-Bosons and Their Coherent States

Fabio Bagarello (Autor)

Buch | Hardcover

XI, 201 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-030-94998-3 (ISBN)

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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.

lt;b>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.

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.

"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)

“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)

Erscheinungsdatum	25.04.2022
Reihe/Serie	Mathematical Physics Studies
Zusatzinfo	XI, 201 p. 5 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	481 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	bi-coherent states • biorthogonal families of vectors • deformed canonical commutation relations • distributions in quantum mechanics • dynamics for non self-adjoint Hamiltonians • eigenvectors and eigenvalues for non self-adjoint Hamiltonians • pseudo-fermions • transition probabilities for non self-adjoint Hamiltonians • truncated pseudo-bosons
ISBN-10	3-030-94998-2 / 3030949982
ISBN-13	978-3-030-94998-3 / 9783030949983
Zustand	Neuware