Corrections to Linear Trajectories from Dual Loop Amplitudes

  • A. D. Karpf
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 13/1974)


Obvious non-unitarity of dual-resonant amplitudes is the reason for going to higher — order (loop) corrections with appropriate square-root threshold singularities. This accounts for unitarity in a perturbative way [1] which means that upon writing the connected part iR of the S-matrix as a sum over all these loop amplitudes the unitarity relation [2] is seen to split up into a perturbative series of relations where internal lines represent δ+(q2−m n 2 )≡θ(qo)δ(q2−m n 2 ), mn being the masses of the intermediate resonances.


Internal Line Perturbative Series Intermediate Resonance Abelian Integral Trajectory Correction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D.J. Gross, A. Neveu, J. Scherk, J. H. Schwarz, Phys. Rev. D2, 697 (1970).ADSGoogle Scholar
  2. 2.
    R. J. Eden, P. V. Landshoff, D. I. Olive, J. C. Polkinghorne, The Analytic S-Matrix, Cambridge University Press, 1966.Google Scholar
  3. 3.
    see e.g. ref. 2, Chapt. 3.6.Google Scholar
  4. 4.
    K. Kikkawa, B. Sakita, M. A. Virasoro, Phys. Rev. 184, 1701 (1969).CrossRefADSMathSciNetGoogle Scholar
  5. 6.
    A. D. Karpf, H. J. Liehl, Factorisation of Dual Loop Amplitudes II, Nucl. Phys. to be published.Google Scholar
  6. 7.
    C. Lovelace, Phys. Lett. 32B, 703 (1970).ADSMathSciNetGoogle Scholar
  7. V. Alessandrini, Nuovo Cimento 2A, 321 (1971).ADSMathSciNetGoogle Scholar
  8. V. Alessandrini, D. Amati, Nuovo Cimento 4A, 793 (1971).ADSMathSciNetGoogle Scholar
  9. A. D. Karpf, H. J. Liehl, H. F. Schuhmacher, Nucl. Phys. B56, 565 (1973).CrossRefADSMathSciNetGoogle Scholar
  10. 8.
    A. Neveu, J. Scherk, Phys. Rev. Dl, 2355 (1970).ADSGoogle Scholar
  11. 9.
    A. D. Karpf, Factorisation of Dual Loop Amplitudes I, Nucl. Phys. to be published.Google Scholar
  12. 10.
    formula (3.11) and (3.12) of ref. 9 for a one-loop amplitude.Google Scholar
  13. 11.
    see e.g. ref. 8 formula (A.l) and (A.3).Google Scholar
  14. 12.
    H. J. Kaiser, F. Kschluhn, E.Wieczorek, Discontinuity of the Regge Trajectory in the DRM I, Berlin Zeuthen preprint PHE 71–3.Google Scholar
  15. 13.
    H. Dorn, H. J. Kaiser, Asymptotic Behaviour of the Planar One Loop Correction…, Berlin-Zeuthen preprint PHE 72–15.Google Scholar
  16. 14.
    J. H. Schwarz, Physics Report 8, 275 (1974).Google Scholar
  17. 15.
    L. Brink, D. Olive, Nucl. Phys. B58, 237 (1973).CrossRefADSGoogle Scholar
  18. 16.
    M. Kaku, K. Kikkawa, Field Theory of Relativistic Strings I, City Univ. N. Y. preprint 1974.Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • A. D. Karpf
    • 1
  1. 1.Institut für ElementarteilchenphysikFreie Universität BerlinGermany

Personalised recommendations