Precisely Predictable Dirac Observables

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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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 ).

• Albert Einstein
• Foldy-Wouthuysen
• Heisenberg
• Potential
• Pseudodifferential
• Schrödinger equations
• Sobolev and Hilbert spaces

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)

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

  Heinz Otto Cordes

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