Skip to main content
Log in

Multiloop amplitudes in additive dual-resonance models

Многопетельные амплитуды в аддитивных дуальных резонансных моделях

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

A technique is developed by which general multiloop amplitudes in additive dual-resonance models can be calculated, with spurious states propagating internally in the loops, however. The result shows the same automorphic structure as has been found in the Veneziano model. The case of the Neveu-Schwarz model is considered in more detail.

Riassunto

Si sviluppa una tecnica per mezzo della quale si possono calcolare ampiezze «multiloop» tipo generale in modelli additivi di risonanze duali, con stati spuri propagantisi internamente alle anse. Il risultato mostra la stessa struttura automorfica che è stata trovata nel modello di Veneziano. Si considera più dettagliatamente il caso del modello di Neveu-Schwarz.

Резюме

Развивается техника, с помощью которой могут быть вычислены общие многопетельные амплитуды в аддитивных дуаляных резонансных модедлях, однако в этих петлях распространяьтся ложные состояния. Полученный результат обладает той же автоморфной структурой, как и следует из модели Венециано. Более подробно рассматривается случай модели Невэ-Шварца.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. For a general review of these problems in the Veneziano model, seeV. Alessandrini, D. Amati, M. Le Bellac andD. Olive:Phys. Rep.,1 c, 269 (1971).

    Article  ADS  Google Scholar 

  2. E. Cremmer andJ. Scherk:Nucl. Phys.,50 B, 222 (1972), and earlier refernces quoted therein.

    Article  ADS  Google Scholar 

  3. L. Clavelli andJ. Shapiro: Rutgers University preprint Rutgers-TH. 02-73 (1973).

  4. A recent review is that ofM. B. Einhorn: invited talk presented at theXVI International Conference on High-Energy Physics 1972 (NAL-Pub-73/14/THY).

  5. C. Lovelace:Phys. Lett.,34 B, 500 (1971);Regge cut theories, inElementary Particles, Proceedings of the Amsterdam Conference 1971, edited byA. G. Tenner andM. J. G. Veltman (Amsterdam, 1972).

    Article  ADS  Google Scholar 

  6. C. Lovelace:Phys. Lett.,40 B, 551 (1972).

    Article  ADS  Google Scholar 

  7. C. Lovelace:Phys. Lett.,32 B, 703 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  8. V. Alessandrini:Nuovo Cimento,2 A, 221 (1971).

    MathSciNet  Google Scholar 

  9. V. Alessandrini andD. Amati:Nuovo Cimento,4 A, 793 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  10. M. Kaku andL. P. Yu:Phys. Rev. D,3, 2992, 3007, 3020 (1971).

    Article  ADS  Google Scholar 

  11. D. Collop: DAMTP preprint 70/39 (1970) (unpublished).

  12. D. Olive:Lectures Given at DAMTP (Cambridge, 1971).

  13. E. Cremmer:Nucl. Phys.,31 B, 477 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  14. A. D. Karpf, H. J. Liehl andH. F. Schumacher: University of Freiburg, preprint UF 9-72 (1972).

  15. C. Lovelace:Phys. Lett.,32 B, 495 (1970).

    ADS  Google Scholar 

  16. D. Olive:Nuovo Cimento,3 A, 399 (1971).

    Article  ADS  Google Scholar 

  17. K. Bardakci andM. B. Halpern:Phys. Rev. D,3, 2493 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Neveu andJ. H. Schwarz:Nucl. Phys.,31 B, 86 (1971);A. Neveu, J. H. Schwarz andC. B. Thorn:Phys. Lett.,35 B, 529 (1971).

    Article  ADS  Google Scholar 

  19. M. B. Halpern:Phys. Rev. D,4, 3082 (1971).

    Article  ADS  Google Scholar 

  20. K. Bardacki:Nucl. Phys.,33 B, 464 (1971).

    Article  ADS  Google Scholar 

  21. H. H. Nickle:Nucl. Phys.,41 B, 215 (1972).

    Article  ADS  Google Scholar 

  22. H. Matsumoto:Nuovo Cimento,10 A, 445 (1972).

    Article  ADS  Google Scholar 

  23. E. Corrigan andC. Montonen:Nucl. Phys.,36 B, 58 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  24. J.-L. Gervais andB. Sakita:Nucl. Phys.,34 B, 477 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  25. For a review of the use of coherent states in the dual resonance model, seeV. Alessandrini et al. (1).

    Article  ADS  Google Scholar 

  26. A good introduction into the subject is given byF. A. Berezin:The Method of Second Quantization (New York, 1966).

  27. R. C. Brower andC. B. Thorn:Nucl. Phys.,31 B, 163 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  28. P. Goddard andR. E. Waltz:Nucl. Phys.,34 B, 99 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  29. J. H. Schwarz:Nucl. Phys.,46 B, 61 (1972).

    Article  ADS  Google Scholar 

  30. L. Brink andD. Olive: CERN preprint TH. 1620 (1973).

  31. K. Kikkawa, B. Sakita andM. A. Virasoro:Phys. Rev.,184, 170 (1969);K. Kikkawa, S. Klein, B. Sakita andM. A. Virasoro:Phys. Rev. D,1, 3258 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  32. IfD=1, the ϕ′s can be taken to be ordinary complex numbers, as inJ. R. Klauder:Ann. of Phys.,11, 123 (1960).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. D. B. Fairlie:Nucl. Phys.,42 B, 253 (1972).

    Article  ADS  Google Scholar 

  34. J. Lehner:Discontinuous Groups and Automorphic Functions (Providence, R. I., 1964).

  35. W. Burnside:Proc. London Math. Soc. (Ser. 1),23, 49 (1891).

    Article  Google Scholar 

  36. A. F. Beardon:Proc. London Math. Soc. (Ser. 3),18, 461 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  37. H. Matsumoto: University of Tokyo, Komaba preprint UT-Komaba 72-7 (1972).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Traduzione a cura della Redazione.

Перевебено ребакциеи.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Montonen, C. Multiloop amplitudes in additive dual-resonance models. Nuov Cim A 19, 69–89 (1974). https://doi.org/10.1007/BF02785444

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02785444

Navigation