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Il Nuovo Cimento (1955-1965)

, Volume 36, Issue 3, pp 968–1001 | Cite as

Quantum field theory of the bootstrap mechanism

  • W. Güttinger
Article

Summary

It is shown that a self-supporting mechanism operates in a conventional quantum field theory which fixes the coupling constants and mass ratios and reproduces the bootstrap mechanism of dispersion theory in some approximation. This self-supporting mechanism is closely related to the Z = 0 physics of composite elementary particles. A restatement of the concept of mass renormalization in other terms is shown to produce finite values for the masses of physical elementary particles in the limit where they become composite. Finiteness of the particle masses is the consequence of a resonance effect. The bootstrap mechanism of field theory and that of dispersion theory turn out to be equivalent to a field theory with direct Fermi interaction, the bare Fermi constant of which vanishes if the theory is to describe interacting particles of finite

Riassunto

Si dimostra che un mecoanismo autosostenuto opera in una teoria quantistica dei oampi convenzionale che fissa le costanti di accoppiamento ed i rapporti di massa e riproduce, con una certa approssimazione, il meccanismo di bootstrap della teoria della dispersione. Questo meccanismo autosostenuto è in stretta relazione con la fisicaZ=0 delle particelle elementari composte. Si dimostra che una riformulazione del concetto di rinormalizzairione della massa con altri termini produce valori flniti per le masse delle particelle elementari flsiche nel limite in oui esse diventano composte. La finitezza delle masse delle particelle è la conseguenza di un effetto di risonanza. Eisulta che il meccanismo di bootstrap della teoria dei campi e quello della teoria della dispersione sono equivalenti ad una teoria dei eampi con interazione di Fermi diretta, la cui pura costante di Fermi tende a zero se la teoria deve descrivere particelle interagenti di massa flnita.

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References

  1. (1).
    G. F. Chew andS. C. Feautschi:Phys. Rev. Lett.,7, 349 (1961).CrossRefGoogle Scholar
  2. (2).
    F. Zachakiasen andC. Zemach:Phys. Rev.,128, 849 (1962).ADSCrossRefGoogle Scholar
  3. (3).
    E. Abeks andC. Zemaoh:Phys: Rev. (1963), preprint;J. S. Ball andD. Y. Wong:Phys. Rev.,133, B 179 (1964);A. Martin:Phys. Rev.,135, B 967 (1964).Google Scholar
  4. (4).
    G. F. Chew andS. Mandelstam:Phys. Rev.,119, 467 (1960).ADSMathSciNetCrossRefGoogle Scholar
  5. (5).
    E. Abeks, F. Zachaeiasen andC. Zemach:Phys. Rev., (1964), preprint;R. H. Capps:Phys. Rev. Lett.,10, 312 (1963) and preprints.Google Scholar
  6. (6).
    M. A. Ruderman:Phys. Rev.,127, 312 (1962);M. A. Rudekmas andS. Gasiorowicz:Nuovo Cimento,8, 861 (1958).ADSMathSciNetCrossRefGoogle Scholar
  7. (7).
    B. Jouvet:Nuovo Cimento,5, 1 (1957).MathSciNetCrossRefGoogle Scholar
  8. (8).
    J. C. Houard andB. Jouvet:Nuovo Cimento,18, 466 (1960);Y. Ataka:Prog. Theor. Phys.,25, 369 (1961);27, 211 (1962);M. T. Vaughn, R. Aabon andR. D. Amado:Phys. Rev.,124, 1258 (1961);A. Salam:Nuovo Cimento,25, 224 (1960);S. Wembekg:Rev.,130, 776 (1963);R. Achabya:Nuovo Cimento,24, 870 (1962);J. S. Dowkeb:Nuovo Cimento,25, 1135 (1962);29, 551 (1963);J. S. Dowker andJ. E. Paton:Nuovo Cimento,30, 450 (1963);M. L. Whippman andI. S. Gerstein: preprint;W. Güttinger, K. Sekine andJ. A. Swieca:Nucl. Phys. (in press) and preprint;B. W. Lee et al.,P. Olesen: preprints.MathSciNetCrossRefGoogle Scholar
  9. (9).
    E. G. P. Rowe:Nucl. Phys.,45, 593 (1963); and preprint.MathSciNetCrossRefGoogle Scholar
  10. (10).
    R. M. Rockmore:Phys. Rev.,132, 878 (1963).ADSMathSciNetCrossRefGoogle Scholar
  11. (11).
    W. Güttinger, K. Sekine andJ. A. Swieca: ref. (8);J. A. Swieca:Thesis, University S. Paulo (1963).Google Scholar
  12. (12).
    W. Güttinger andJ. A. Swieca;Zeite. f. Naturfors.,16 a, 1265 (1961).ADSGoogle Scholar
  13. (13).
    S. Okubo andD. Feldman:Phys. Mev.,117, 279 (1960).ADSMathSciNetGoogle Scholar
  14. (14).
    H. Lehmann, K. Symanzik andW. Zimmermann:Nuovo Cimento,2, 425 (1955).MathSciNetCrossRefGoogle Scholar
  15. (15).
    K. Nismijima:Phys. Rev.,133, B 204 (1964);122, 298 (1961);E. Haag:Phys. Rev.,112, 669 (1958).ADSCrossRefGoogle Scholar
  16. (16).
    Cf. alsoF. Bopp:Zeits. f. Phys.,171, 90 (1963).ADSMathSciNetCrossRefGoogle Scholar
  17. (17).
    L. D. Landau: inNiels Bohr and the Development of Physics, edited byW. Pauli (London, 1955).Google Scholar
  18. (18).
    J. S. Ball andD. Y. Wong: ref. (3);H. Mitazawa andH. Sugawaka:Progr. Theor. Phys. (1963), preprint.Google Scholar
  19. (19).
    K. W. Chen, A. A. Cone et al.:Phys. Rev. Lett.,11, 561 (1963).ADSCrossRefGoogle Scholar
  20. (20).
    H.-P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder andK. Yamazaki:Zeits, f. Naturfors.,14 a, 441 (1959);T. Nambu andG. Jona-Lasinio:Phys. Rev.,122, 345 (1961).ADSGoogle Scholar
  21. (2l).
    M. Suzuki:Progr. Theor. Phys.,30, 672 (1963); and preprints.Google Scholar
  22. (22).
    G. Feinberg andA. Pats:Phys. Rev.,133, B 477 (1964).ADSCrossRefGoogle Scholar
  23. (23).
    L. S. Lim Phys. Rev.,125, 761 (1962).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1965

Authors and Affiliations

  • W. Güttinger
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of MünchenMünchen

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