Born-Jordan Quantization

Theory and Applications
Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-80236-7
Verlag: Springer International Publishing

Buch, Englisch, Band 182, 226 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 371 g

Reihe: Fundamental Theories of Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

De Gosson, Maurice A.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

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).