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Il Nuovo Cimento A (1971-1996)

, Volume 46, Issue 2, pp 223–280 | Cite as

Nonlinear theory with hermitean spinor field operators

  • H. P. Dürr
  • F. Wagner
Article

Summary

The nonlinear spinor theory is formulated in terms of Hermitean spinor field operators. The functional equations for the generators of matrix elements for the time-ordered and normal-ordered products for these operators, and the explicit form of the resulting systems of coupled differential and integral equations for the matrix elements are derived. A graphical description of these equations is given, which proves very useful for practical computations. Masses and coupling constants approximately derived in earlier papers are recalculated, and equations for the fermion and boson propagators are given.

Нелинейная теория с эрмитовскими спинорными операторами поля

Резюме

Сформулирована нелинейная спинорная теория с эрмитовскими спиновыми операторами поля. Выведены функциональные уравнения для матричных элементов операторов пождения дляT- иN-упорядочненных произведений этих операторов, и для матричных элементов получено явное выражение систем связанных дифференциальных и интегральных уравнений. Приводится графическое описание этих уравнений, которое оказывается очень полезным для практических вычислений. Пересчитаны массы и константы связи, приблизительно вычисленные в предыдуших работах и получены уравнения для фермионного и бозонного пропагаторов.

Riassunto

Si formula una teoria spinoriale non lineare in base ad operatori di campo spinoriali hermitiani. Si deducono le equazioni funzionali dei generatori degli elementi di matrice per i prodotti ordinati nel tempo ed ordinati normalmente di questi operatori, e si deriva la forma esplicita dei sistemi di equazioni differenziali ed integrali accoppiate degli elementi di matrice che ne risultano. Si espone una descrizione grafica di queste equazioni, che si dimostra molto utile nei calcoli pratici. Si ricalcolano le masse e le costanti di accoppiamento dedotte approssimativamente negli articoli precedenti, e si danno le equazioni dei propagatori fermionici e bosonici.

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References

  1. (1).
    Seee g.,J. Schwinger:Phys. Rev.,91, 713 (1953).MathSciNetCrossRefADSGoogle Scholar
  2. (2).
    H. P. Dürr:Proceedings of the Seminar on Unified Theories (Rochester, 1963).Google Scholar
  3. (3).
    N. N. Bogoliubov:Report at the Utrecht Conference on Many-Body Problem (June 1960).Google Scholar
  4. (4).
    H. P. Dürr andW. Heisenberg:Nuovo Cimento,37, 1446, 1487 (1965).CrossRefGoogle Scholar
  5. (5).
    H. Stumpf, F. Wagner andF. Wahl:Zeits. f. Naturforschg.,19a, 1254 (1964).MathSciNetADSGoogle Scholar
  6. (6).
    F. Wagner: Dissertation 1966, University of München.Google Scholar
  7. (7).
    H. Rampacher, H. Stumpf andF. Wagner:Fortschr. d. Phys.,13, 385 (1965).MathSciNetCrossRefADSGoogle Scholar
  8. (8).
    B. L. van der Waerden:Die gruppentheoretische Methode in der Quantenmechanik (Berlin, 1932).Google Scholar
  9. (9).
    M. Fierz:Zeits. f. Phys.,104, 553 (1937).CrossRefADSGoogle Scholar
  10. (10).
    H. P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder andK. Yamazaki:Zeits. f. Naturforschg.,14a, 441 (1959); There one finds a list of earlier papers.ADSGoogle Scholar
  11. (11).
    H. P. Dürr:Zeits. f. Naturforschg.,16 a, 327 (1961).ADSGoogle Scholar
  12. (12).
    For a review seee.g. H. P. Dürr: Matscience Lectures (1963);W. Heisenberg:Introduction to the Unified Theory of Elementary Particles, Lectures München SS 1965, to be published.Google Scholar
  13. (13).
    R. Haag: Lille lectures 1957;Phys. Rev.,112, 669 (1958);Ann. d. Phys.,11, 29 (1963).Google Scholar
  14. (14).
    K. Symanzik:Zeits. f. Naturforschg.,9 a, 809 (1954).MathSciNetADSGoogle Scholar
  15. (15).
    H. Umezawa andS. Kamefuchi:Progr. Theor. Phys.,6, 543 (1951);G. Källén:Helv. Phys. Acta,25, 417 (1952);H. Lehmann:Nuovo Cimento,11, 342 (1954).MathSciNetCrossRefADSGoogle Scholar
  16. (16).
    H. Roos: Dissertation München, in preparation.Google Scholar
  17. (17).
    W. Heisenberg:Nachr. Gött. Akad. Wiss.,111 (1953);Zeits. f. Naturforschg.,9 a, 292 (1954); see alsoK. Symanzik: Dissertation Göttingen (1954).Google Scholar
  18. (18).
    P. T. Matthews andA. Salam:Proc. Roy. Soc. Ld., A221, 128 (1954).MathSciNetCrossRefADSGoogle Scholar
  19. (19).
    H. Mitter:Nuovo Cimento,38, 1040 (1965).CrossRefGoogle Scholar
  20. (20).
    F. J. Dyson:Phys. Rev.,90, 994 (1953);91, 421, 1543 (1953);W. Heisenberg:Nachr. Gött. Akad.,27 (1956).CrossRefADSGoogle Scholar
  21. (21).
    H. Joos:Fortschr. d. Phys.,10, 65 (1962).CrossRefADSGoogle Scholar
  22. (22).
    J. Dhar andY. Katayama:Nuovo Cimento,36, 533 (1965).MathSciNetCrossRefGoogle Scholar
  23. (23).
    H. Mitter:Zeits. f. Naturforschg.,20 a, 1505 (1965); andW. Heisenberg: loc. cit. (12) For a review seee. g. H. P. Dürr: Matscience Lectures (1963).MathSciNetADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1966

Authors and Affiliations

  • H. P. Dürr
    • 1
  • F. Wagner
    • 1
  1. 1.Max-Planck-Institut für Physik und AstrophysikMünchen

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