Maurice A. de Gosson

Born-Jordan Quantization

Theory and Applications

• Broschiertes Buch

Produktbeschreibung

This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan scheme is used. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born-Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.

Produktdetails

• Fundamental Theories of Physics 182
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-80236-7
• Softcover reprint of the original 1st ed. 2016
• Seitenzahl: 240
• Erscheinungstermin: 30. März 2018
• Englisch
• Abmessung: 235mm x 155mm x 14mm
• Gewicht: 373g
• ISBN-13: 9783319802367
• ISBN-10: 3319802364
• Artikelnr.: 53584055

Autorenporträt

Maurice de Gosson is a research professor at the Univer-sity of Vienna. He has held various visiting positions at prestigious Universities(Yale, Boulder, Tel Aviv).

Inhaltsangabe

Born-Jordan Quantization: Physical Motivation: On the Quantization Problem.- Quantization of Monomials.- Basic Hamiltonian Mechanics.- Wave Mechanics and the Schrödinger Equation.- Mathematical Aspects of Born-Jordan Quantization: The Weyl Correspondence.- The Cohen Class.- Born-Jordan Quantization.- Shubin's Pseudo-Differential Calculus.- Born-Jordan Pseudo-Differential Operators.- Weak Values and the Reconstruction Problem.- Some Advanced Topics: Metaplectic Operators.- Symplectic Covariance Properties.- Symbol Classes and Function Spaces.

Rezensionen

"In this book, the Born-Jordan and Weyl quantizations are confronted and discussed into details. ... The book is well written and in great part self-contained, it is intended as an introduction to Born-Jordan quantization both for physicists and mathematicians. The subject is analyzed both from the physical and the mathematical point of view." (Giovanni Rastelli, zbMATH 1338.81014, 2016)