Born-Jordan Quantization
Theory and Applications
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Beschreibung
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.
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.
Demonstrates the superiority of the Born-Jordan scheme as the only consistent approach to quantization Written by a highly respected expert in quantum theory Provides in depth analysis of both mathematical and conceptual aspects Includes supplementary material: sn.pub/extras
Autor*in
Maurice A. de Gosson
Themen in »Born-Jordan Quantization«
Grossmann-Royer operator Heisenberg-Weyl operator Phase-space representation of quantum mechanics Quantization schemes Shubin prescription Symmetry properties of quantum systems Theory of pseudodifferential operators Born-Jordan-Wigner transform
Stimmen zu »Born-Jordan Quantization«
“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)
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