| Document Type
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BL
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| Record Number
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650015
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| Doc. No
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dltt
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| Main Entry
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Gosson, Maurice de
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| Title & Author
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Born-Jordan quantization : : theory and applications /\ Maurice A. de Gosson
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| Series Statement
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Fundamental theories of physics,; 182
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| Page. NO
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1 online resource (xiii, 226 pages).
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| ISBN
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9783319279022
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: 3319279025
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9783319279008
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3319279009
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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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
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| Abstract
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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
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| Subject
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Mathematical physics.
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| Subject
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Operator-valued functions.
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| Dewey Classification
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530.15
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| LC Classification
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QC20
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| Added Entry
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Ohio Library and Information Network.
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