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Precisely Predictable Dirac Observables

  • Book
  • © 2007

Overview

Authors:
  1. Heinz Otto Cordes

    1. Professor Emeritus, Department of Mathematics, University of California, Berkeley, U.S.A.

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  • A successful attempt to provide a Clean Observable Theory for Dirac’s Equation, free of contradictions like "Zitterbewegung"
  • The existence of an accurate split between physical states belonging to the electron and to the positron is discussed, as well as the fact that precisely predictable observables must preserve this split

Part of the book series: Fundamental Theories of Physics (FTPH, volume 154)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Dirac Observables and ψdo-s

    • Heinz Otto Cordes
    Pages 1-35

  3. Why Should Observables be Pseudodifferential?

    • Heinz Otto Cordes
    Pages 37-53

  4. Decoupling with ψdo-s

    • Heinz Otto Cordes
    Pages 55-81

  5. Smooth Pseudodifferential Heisenberg Representation

    • Heinz Otto Cordes
    Pages 83-116

  6. The Algebra of Precisely Predictable Observables

    • Heinz Otto Cordes
    Pages 117-148

  7. Lorentz Covariance of Precise Predictability

    • Heinz Otto Cordes
    Pages 149-191

  8. Spectral Theory of Precisely Predictable Approximations

    • Heinz Otto Cordes
    Pages 193-235

  9. Dirac and Schrödinger Equations; a Comparison

    • Heinz Otto Cordes
    Pages 237-257

  10. Back Matter

    Pages 259-275
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Keywords

About this book

In this book we are attempting to o?er a modi?cation of Dirac’s theory of the electron we believe to be free of the usual paradoxa, so as perhaps to be acceptable as a clean quantum-mechanical treatment. While it seems to be a fact that the classical mechanics, from Newton to E- stein’s theory of gravitation, o?ers a very rigorous concept, free of contradictions and able to accurately predict motion of a mass point, quantum mechanics, even in its simplest cases, does not seem to have this kind of clarity. Almost it seems that everyone of its fathers had his own wave equation. For the quantum mechanical 1-body problem (with vanishing potentials) let 1 us focus on 3 di?erent wave equations : (I) The Klein-Gordon equation 3 2 2 2 2 (1) ? ?/?t +(1??)? =0 , ? = Laplacian = ? /?x . j 1 This equation may be written as ? ? (2) (?/?t?i 1??)(?/?t +i 1??)? =0 . Hereitmaybenotedthattheoperator1??hasawellde?nedpositive square root as unbounded self-adjoint positive operator of the Hilbert 2 3 spaceH = L (R ).

Reviews

From the reviews:

"In this very interesting book, the author proposes a modification of Dirac’s theory of the electron, that he believes to be free of the systematic well-known difficulties that give rise to the usual paradoxes. … the direction he describes in this book is promising, and will hopefully open the way to the construction of a more general framework." (Alberto Parmeggiani, Mathematical Reviews, Issue 2008 j)

"In this book Heinz Otto Cordes tries to make a contribution from the point of view of a mathematician, and it is certainly an interesting one. … it is very pleasant reading for the more mathematically inclined person, and those with some interest in physics will enjoy the many insightful remarks about quantum mechanics immersed in the text. I warmly recommend this book to mathematicians and mathematical physicists interested in the Dirac equation." (Bernd Thaller, SIAM Review, Vol. 50 (2), 2008)

Authors and Affiliations

  • Professor Emeritus, Department of Mathematics, University of California, Berkeley, U.S.A.

    Heinz Otto Cordes

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