Born-Jordan Quantization

Theory and Applications

Maurice A. de Gosson (Autor)

Buch | Softcover

XIII, 226 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-80236-7 (ISBN)

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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.

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).

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.

"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)

Erscheinungsdatum	18.06.2018
Reihe/Serie	Fundamental Theories of Physics
Zusatzinfo	XIII, 226 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	373 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Born-Jordan-Wigner transform • Born- Jordan- Wigner transform • Born--Jordan--Wigner transform • Born-Jordan-Wigner transform • 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
ISBN-10	3-319-80236-4 / 3319802364
ISBN-13	978-3-319-80236-7 / 9783319802367
Zustand	Neuware