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Families as radial excitations

  • C. Kopper
Article

Summary

It is shown that the qualitative features of the experimental data on the mass spectrum and spatial extension of the charged leptons and quarks can be reproduced by the eigenstates of relativistic wave equations if there are strongly attractive renormalizable forces which are asymptotically free (or undercritical). Beyond one has to assume that the boundary condition on the running coupling is different for different bound states.

PACS. 11.10

Field theory 

Семейства, как радиальные возбуждения

Резюме

Показывается, что качественные особенности Экспериментальных данных для спектров масс и пространственной протяженности заряженных лептонов и кварков могут быть воспроизведены с помошью собственных состояний релятивистских волновых уравнений, если сушествуют сильные притягиваюшие перенормируемые силы, которые являются асимптотически свободными (или докритическими). Кроме того предполагается, что граничное условие для варьируемой связи является различным для различных связанных состояний.

Riassunto

Si mostra che le caratteristiche qualitative dei dati sperimentali sullo spettro di massa e l’estensione spaziale dei leptoni carichi e dei quark si possono riprodurre mediante gli autostati delle equazioni d’onda relativistiche se ci sono forze rinormalizzabili fortemente attrattive che sono asintoticamente libere (o sottocritiche). Inoltre bisogna assumere che la condizione al contorno sull’accoppiamento corrente è diversa per i diversi stati legati.

References

  1. (1).
    S. L. Glashow, J. Iliopoulos andL. Maiani:Phys. Rev. D,2, 1285 (1970).CrossRefADSGoogle Scholar
  2. (2).
    C. Bouchiat, J. Iliopoulos andPh. Meyer:Phys. Lett. B,38, 44 (1972).CrossRefGoogle Scholar
  3. (3).
    V. Višnjić-Triantafillou:Phys. Lett. B,95, 47 (1980)CrossRefADSGoogle Scholar
  4. (4).
    Ch. Kopper andH. P. Dürr:Nuovo Cimento A,66, 427 (1981)CrossRefADSGoogle Scholar
  5. (5).
    O. W. Greenberg andJ. Sucher:Phys. Lett. B,99, 339 (1981).CrossRefADSGoogle Scholar
  6. (6).
    S. Yamada: inProceedings of the 1983 International Symposium on Lepton and Photon Interactions (Cornell University Press, Ithaca, N. Y., 1984).Google Scholar
  7. (7).
    C. Itzykson andJ. B. Zuber:Quantum Field Theory (McGraw-Hill, New York, N. Y., 1980), Chapt. 2.Google Scholar
  8. (8).
    H. Narnhofer:Acta Phys. Austriaca,40, 306 (1974).MathSciNetGoogle Scholar
  9. (10).
    H. A. Bethe andE. E. Salpeter:Quantum Mechanics of One-and Two-Electron Atoms (Springer-Verlag, New York, N. Y., 1957), Sect. 14.CrossRefMATHGoogle Scholar
  10. (11).
    W. Pieper andW. Greiner:Z. Phys.,218, 327 (1969)CrossRefADSGoogle Scholar
  11. (12).
    Ch. Kopper:Nuovo Cimento A,93, 99 (1986).CrossRefADSGoogle Scholar
  12. (13).
    K. M. Case:Phys. Rev.,80, 977 (1950).CrossRefGoogle Scholar
  13. (15).
    F. J. Dyson:Phys. Rev.,75, 1736 (1949)MathSciNetCrossRefADSMATHGoogle Scholar
  14. (16).
    N. Nakanishi:Suppl. Prog. Theor. Phys.,43, 1 (1969).CrossRefADSMATHGoogle Scholar
  15. (17).
    C. Itzykson andJ. B. Zuber:Quantum Field Theory (McGraw-Hill, New York, N. Y., 1980), Chapt. 10, from which we also take our conventions on propagators, Feynman rules, etc.Google Scholar
  16. (18).
    S. Drell andT. D. Lee:Phys. Rev. D,5, 1738 (1972).CrossRefADSGoogle Scholar
  17. (19).
    G. T. Bodwin andD. R. Yennie:Phys. Rep.,43, 267 (1978), Chapt. 3.CrossRefADSGoogle Scholar
  18. (20).
    H. P. Dürr:Nuovo Cimento A,78, 265 (1983).Google Scholar
  19. (22).
    H. Saller:Nuovo Cimento A,79, 333 (1984).CrossRefADSGoogle Scholar
  20. (23).
    E. Derman:Phys. Rev. D,23, 1623 (1981).CrossRefADSGoogle Scholar
  21. (24).
    K. Aoki, Z. Hioki, R. Kawabe, M. Konuma andT. Muta:Prog. Theor. Phys. Suppl.,73, 1 (1982).CrossRefADSGoogle Scholar
  22. (25).
    G. C. Wick:Phys. Rev.,96, 1124 (1954)MathSciNetCrossRefADSMATHGoogle Scholar
  23. (26).
    E. zur Linden andH. Mitter:Nuovo Cimento B,61, 389 (1969).CrossRefADSGoogle Scholar
  24. (27).
    K. D. Rothe:Phys. Rev.,170, 1548 (1968).CrossRefADSGoogle Scholar
  25. (28).
    S. Mandelstam:Proc. R. Soc. London, Ser. A,233, 248 (1955).MathSciNetCrossRefADSMATHGoogle Scholar
  26. (29).
    M. Fischler andJ. Oliensis:Phys. Lett. B,119, 385 (1982).CrossRefADSGoogle Scholar
  27. (30).
    J. Bartholomew et al.:Nucl. Phys. B,230, 222 (1983).CrossRefADSGoogle Scholar
  28. (*).
    There is also an argument that a confining BS kernel should be re-defined by an additive constant (31).CrossRefADSGoogle Scholar
  29. (31).
    D. Gromes:Z. Phys. C,11, 147 (1981).CrossRefADSGoogle Scholar
  30. (32).
    M. B. Halpern:Ann. Phys. (N. Y.),39, 351 (1966).CrossRefADSGoogle Scholar
  31. (33).
    C. Itzykson andJ. B. Zuber:Quantum Field Theory (McGraw-Hill, New York, N. Y., 1980), p. 493.Google Scholar
  32. (34).
    M. J. Levine, J. Wright andJ. A. Tjon:Phys. Rev.,157, 1416 (1967)CrossRefADSGoogle Scholar
  33. (35).
    Ch. Kopper:Phys. Lett. B,155, 409 (1985).CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • C. Kopper
    • 1
    • 2
  1. 1.Max-Planck-Institut für Physik und AstrophysikWerner Heisenberg Institut für PhysikMünchen 40BRD
  2. 2.Instituut voor Theoretische FysicaRijksuniversiteitTA UtrechtThe Netherlands

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