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Zur Theorie der Elementarteilchen

  • H.-P. Dürr
  • W. Heisenberg
  • H. Mitter
  • S. Schlieder
  • K. Yamazaki
Part of the Gesammelte Werke / Collected Works book series (HEISENBERG, volume A / 3)

Abstract

The equation \({\gamma_{\nu}}\frac{\partial}{{\partial{x_{\nu}}}}\psi\pm{l^2}{\gamma_{\mu}}{\gamma_5}\psi\left({\bar{\psi}{\gamma_{\mu}}{\gamma_5}\psi}\right)=0 \) is analysed with respect to the following consequences. In I the group theoretical structure of the equation is studied. The equation is invariant under a number of continous transformations: the inhomogeneous Lorentzgroup, the transformations of Pauli, Gürsey and Touschek, and the scale transformation [x → η x orψ → η 3/2 ψ (x η, l η)]. The Pauli-Gürsey group is used for the interpretation of the isospin; the γ 3-transformation of Touschek establishes a quantum number I N, and the scale transformation leads to a quantum number l N, which both are connected with the baryonic and the leptonic number. The strangeness s = l N - l Q is suggested to be connected with the discrete groups of the equation and could then be defined and conserved only modulo 4. Of the discrete groups only the well known transformations P, C and T and the reversal of l(l → - l) are briefly discussed. In II the vacuum expectation values of products of two field operators are studied. These values are considered to be only in a first approximation invariant under the Isospin-group. The deviations from the Pauli-Gürsey symmetry in higher approximations are supposed to be due to the replacement of the state “vacuum” by an idealised state “world”, which possesses an infinite isospin; the strange particles are consequently interpreted as states which “borrow” an isospin 1/2 or 1 from the ground state “world”. The concept of “One particle-wavefunctions” is discussed in III. The fermions of finite mass belong to wavefunctions obeying a Klein-Gordon-spinor equation instead of a Dirac equation. The connection with the conventional formalism of the Dirac equation is treated in detail. The process of ^-conjugation springing from these discussions is used for a variation of the methods of approximation needed later on for the determination of mass values and the pion-nucleon coupling constant.

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Literatur

  1. 1.
    W. Heisenberg, Nachr. d. Gött. Akad. d. Wiss. 1953, S. 111.Google Scholar
  2. 2.
    W. Heisenberg, Z. Naturforschg. 9a, 292 [1954].Google Scholar
  3. 3.
    W. Heisenberg, F. Kortel u. H. Mitter, Z. Naturforschg. 10a, 425 [1955], im folgenden auch als [3] zitiert.Google Scholar
  4. 4.
    W. Heisenberg, Z. Phys. 144, 1 [1956].CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    W. Heisenberg, Nachr. d. Gött. Akad. d. Wiss. 1956, S. 27.Google Scholar
  6. 6.
    R. Ascoli U.W. Heisenberg, Z.Naturforschg. 12a, 177[1957].Google Scholar
  7. 7.
    W. Heisenberg, Rev. Mod. Phys. 29. 269 [1957].CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    W. Heisenberg, Nuclear Phys. 4, 532 [1957]CrossRefzbMATHGoogle Scholar
  9. 8a.
    W. Heisenberg, Nuclear Phys.**5, 195 [1958]. Von früheren Arbeiten, die von einer nichtlinearen Spinortheorie Gebrauch machen, seien erwähnt:CrossRefzbMATHGoogle Scholar
  10. 9.
    E. Fermi, Z. Phys. 88, 161 [1934].CrossRefGoogle Scholar
  11. 10.
    W. Heisenberg, Z. Phys. 101, 533 [1936].CrossRefGoogle Scholar
  12. 11.
    D. Iwanenko, Phys. Z. Sowjetunion 13, 141 [1938], undzbMATHGoogle Scholar
  13. 12.
    D. Iwanenko u. A. Brodsky, C. R. Acad. Sci. USSR 84, 683 [1952].Google Scholar
  14. 13.
    F. Gürsey, Nuovo Cim. 7, 411 [1958].CrossRefzbMATHGoogle Scholar
  15. 14.
    W. Pauli, Nuovo Cim. 6, 204 [1957].CrossRefzbMATHMathSciNetGoogle Scholar
  16. 15.
    W. Heisenberg u. W. Pauli, On the Isospin group in the theory of elementary particles. Preprint 1958.Google Scholar
  17. 16.
    W. Heisenberg, Proceedings of the Conference on High Energy Physics (CERN, Geneva 1958).Google Scholar
  18. 18.
    B. Touschex, Nuovo Cim. 5, 1281 [1957].CrossRefGoogle Scholar
  19. 19.
    B. D’Espagnat u. J. Prentki, Nuclear Phys. 1, 33 [1956].MathSciNetGoogle Scholar
  20. 21.
    G. Wentzel, Sixth Annual Rochester Conference 1956, S. VIII-16 und Phys. Rev. 101, 1214 [1956].Google Scholar
  21. 22.
    T. W. B. Kibble u J. C. Polkinghorne, Nuovo Cim. 8, 74 [1958].CrossRefMathSciNetGoogle Scholar
  22. 24.
    R. P. Feynman u. M. Gell-Mann, Phys. Rev. 109, 193 [1958].CrossRefzbMATHMathSciNetGoogle Scholar
  23. *.
    Ann. b. d. Korr: vgl. schon Géhéniau, Mécanique ondulatoire de l’Électron et du Photon, Gauthier-Villars, Paris 1938.Google Scholar
  24. *a.
    **Korr Die wesentlichen Resultate dieses Abschnitts sind auch von G. Marx, Nuclear Phys. 9, 337 [1958]CrossRefGoogle Scholar
  25. *b.
    Korr Die wesentlichen Resultate dieses Abschnitts sind auch von G. Marx, Nuclear Phys.**10, 468 [1959] gefunden worden.CrossRefGoogle Scholar
  26. 25.
    K. Symanzik, Göttinger Dissertation, 1954.Google Scholar
  27. 30.
    E. Freese, Z. Naturforsch. 8a, 776 [1953].Google Scholar
  28. 34.
    S. Fubini u. W. E. Thirring, Phys. Rev. 105, 1382 [1957].CrossRefzbMATHMathSciNetGoogle Scholar
  29. 35.
    Vgl. z. B. W. Pauli Diskussionsbemerkung: High energy conference at CERN 1958, S. 123.Google Scholar
  30. 36.
    R. Haag. Phys. Rev. 112, 669 [1958] und Colloqu. Internationale sur les Problemes Mathem. de la Théorie Quantique des Champs, Lille 1957, herausgeg. von CNSR, Paris 1958.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • H.-P. Dürr
    • 1
  • W. Heisenberg
    • 1
  • H. Mitter
    • 1
  • S. Schlieder
    • 1
  • K. Yamazaki
    • 1
  1. 1.Max-Planck-Institut für Physik und AstrophysikMünchenDeutschland

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