Summing All the Eikonal Graphs

  • H. M. Fried
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 39)


During the past year there has been some progress in al old problem of eikonal physics, that of estimating the high-energy contributions of all eikonal pionization graphs (tower plus non- planar) in some relevant Lagrangian field theory. Since so much material has already been presented concerning non-Abelian physics at this Summer Institute, and partly to remind us that much high- energy phenomenology is still couched in the language of non-non- Abelian theories, I will try to present a very brief description of this recent work1). There is also a personal reason for this choice: at Cargèse, five years ago, I presented a critique of the then-fashionable Cheng-Wu “explanation” of rising total cross sections2); and now it is most satisfying to be more constructive, to point out in the context of an approximate, semi-classical type of computation that sums over all eikonal graphs, which features of their calculation remain and which must be changed.


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  1. 1).
    H. Moreno and H.N. Fried, Nice Preprint NTH 77/5.Google Scholar
  2. 2).
    H. Cheng and T.T.Wu, Phys.Rev.Letters 24, 1455 (1970); S-J Chang and T-M Yan, Phys.Rev. D4, 537 (1971).ADSCrossRefGoogle Scholar
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    Rather extensive discussions and applications of the fundamental Bloch-Nordsieck approximation may be found in: H.M. FRIED, “Functional Methods and Models in Quantum Field Theory”, M.I.T. Press, Cambridge (1972).Google Scholar
  4. 4).
    R. Blankenbecler and H.M. Fried, Phys. Rev. D8, 678 (1973).ADSGoogle Scholar
  5. 5).
    M. Levy and J. Sucher, Phys. Rev. D2, 1716 (1970).ADSGoogle Scholar
  6. 6).
    H. Moreno and H.M. Fried, Phys. Rev. D12, 2031 (1975).ADSCrossRefGoogle Scholar
  7. 7).
    D. Amati, M. Le Bellac, G. Marchesini and M. Ciafaloni, Nucl.Phys. B112 (1976) 107.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • H. M. Fried
    • 1
    • 2
  1. 1.Physique ThéoriqueUniversité de NiceFrance
  2. 2.Physics DepartmentBrown UniversityProvidenceUSA

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