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Born-Jordan Quantization

Theory and Applications

  • Maurice A. de Gosson

Part of the Fundamental Theories of Physics book series (FTPH, volume 182)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Maurice A. de Gosson
    Pages 1-6
  3. Born–Jordan Quantization: Physical Motivation

    1. Front Matter
      Pages 7-7
    2. Maurice A. de Gosson
      Pages 9-21
    3. Maurice A. de Gosson
      Pages 23-35
    4. Maurice A. de Gosson
      Pages 37-55
    5. Maurice A. de Gosson
      Pages 57-70
  4. Mathematical Aspects of Born–Jordan Quantization

    1. Front Matter
      Pages 71-71
    2. Maurice A. de Gosson
      Pages 73-94
    3. Maurice A. de Gosson
      Pages 95-111
    4. Maurice A. de Gosson
      Pages 113-127
    5. Maurice A. de Gosson
      Pages 129-145
    6. Maurice A. de Gosson
      Pages 147-159
    7. Maurice A. de Gosson
      Pages 161-170
  5. Some Advanced Topics

    1. Front Matter
      Pages 171-171
    2. Maurice A. de Gosson
      Pages 173-184
    3. Maurice A. de Gosson
      Pages 185-197
    4. Maurice A. de Gosson
      Pages 199-215
  6. Back Matter
    Pages 217-226

About this book

Introduction

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.

Keywords

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”

Authors and affiliations

  • Maurice A. de Gosson
    • 1
  1. 1.Universität WienWienAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27902-2
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-27900-8
  • Online ISBN 978-3-319-27902-2
  • Series Print ISSN 0168-1222
  • Series Online ISSN 2365-6425
  • Buy this book on publisher's site
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