Advertisement

The Physical Basis of the Asymptotic Estimates in Perturbation Theory

  • G. Parisi
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 39)

Abstract

During last year, the asymptotic behaviour in K of the Kth order of the perturbative expansion has been widely investigated with remarkable success1–3. If the interaction is superrenormalizable, the problem has been solved for both interacting bosons4, 5 and fermions6–8: of course technical details may change from theory to theory. When the interaction is renormalizable new difficulties arise9, 10; they are not completely understood at the present moment.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.N. Lipatov, JEPT 72 (1977) 411MathSciNetGoogle Scholar
  2. 2.
    E. Brezin, J.C. Le Guillou, J. Zinn-Justin, Phys.Rev. D15 (1977) 1544ADSGoogle Scholar
  3. 3.
    G. Parisi, Phys.Lett. 66B (1977) 167CrossRefGoogle Scholar
  4. 4.
    E. Brezin, J.C. Le Guillou, J. Zinn-Justin, Phys.Rev. D15 (1977) 1558ADSGoogle Scholar
  5. 5.
    C. Itzykson, G. Parisi, J.B. Zuber, Phys.Rev.Letters 38 (1977) 306ADSCrossRefGoogle Scholar
  6. 6.
    G. Parisi, Phys.Lett. 66B (1977) 382CrossRefGoogle Scholar
  7. 7.
    C. Itzykson, G. Parisi, J.B. Zuber, Saclay preprint DPh/T 77/27 (Phys.Rev. D to be published)Google Scholar
  8. 8.
    R. Balian, C. Itzykson, G. Parisi, J.B. Zuber, Saclay preprint DPh/T 77/92Google Scholar
  9. 9.
    G. ’t Hooft, Lectures given at Erice, July 1977Google Scholar
  10. 10.
    B. Lautrup, Phys.Lett. 69B (1977) 109CrossRefMathSciNetGoogle Scholar
  11. 11.
    S. Graffi, V. Grecchi, B. Simon, Phys.Lett. 32B (1970) 631CrossRefMathSciNetGoogle Scholar
  12. 12.
    J.D. Eckmann, J. Magnen, R. Seneor, Comm. Math. Phys. 39 (1975) 251ADSCrossRefMathSciNetGoogle Scholar
  13. 13.
    P. Renuard, preprint Ecole Polytechnique Palaiseau, n°A247 1076 (1976)Google Scholar
  14. 14.
    J.J. Loeffel “Workshop on Pade Approximants”, Ed. D. Bessis, J. Gilewiczond, P. Merry CEA (1976)Google Scholar
  15. 15.
    J.C. Le Guillou, J. Zinn-Justin, Phys.Rev.Lett. 39 (1977)95ADSCrossRefGoogle Scholar
  16. 16.
    G. Parisi, Phys.Lett. 65 B (1977) 329CrossRefGoogle Scholar
  17. 17.
    G. Parisi, Lectures given at the Cargèse Summer Institute (1976)Google Scholar
  18. 18.
    J.S. Langer, Ann. of Phys. 41 ( 1967 ) 108ADSCrossRefGoogle Scholar
  19. 19.
    H. Lieb, Rev. Mod. Phys. 49 (1977) 137Google Scholar
  20. 20.
    See for example L. Landau, E. Lifschitz, Mécanique Quantique Ed. Mir, Moscou (1970)Google Scholar
  21. 21.
    A.A. Belavin, A.M. Poliakov, A.S. Schwartz, Yu S. Tyupkin, Phys.Lett. 59B (1977) 85CrossRefGoogle Scholar
  22. 22.
    G. ’t Hooft, Phys.Rev.Lett. 37 (1976) 8ADSCrossRefGoogle Scholar
  23. 23.
    A.M. Poliakov, Nucl. Phys. B120 (1977) 429ADSCrossRefGoogle Scholar
  24. 24.
    E. Brezin, G. Parisi, J. Zinn-Justin, Saclay Preprint DPh/T 77/16 (Phys.Rev. D to be published)Google Scholar
  25. 25.
    T. Banks, C.N. Bender, T.T. Wu, Phys.Rev. D8 (1973) 3346MathSciNetGoogle Scholar
  26. 26.
    L.D. Landau, A.A. Abrikosov, I.M. Khalatnikow, Doklady Acad. Nauk URSS 95 (1954) 773Google Scholar
  27. 27.
    C.M. Bender, T.T. Wu, Phys.Rev.Lett. 37 (1976) 117ADSCrossRefMathSciNetGoogle Scholar
  28. 28.
    G. Parisi, Phys.Lett. 68B (1977) 361CrossRefGoogle Scholar
  29. 29.
    N.N. Khury, Phys.Rev. D12 (1975) 2298 and Rockfeller Univ. Preprint COO 2232B 131ADSCrossRefMathSciNetGoogle Scholar
  30. 30.
    C.G. Callan, Phys.Rev. D2 (1970) 1541ADSCrossRefGoogle Scholar
  31. 31.
    K. Symanzik, Comm.Math.Phys. 18 (1970) 227ADSCrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    G. Parisi, Lectures given at the Cargèse Summer School (1973) Columbia University PreprintGoogle Scholar
  33. 33.
    G. Parisi, Nuovo Cimento, 21A (1974) 179ADSCrossRefGoogle Scholar
  34. 34.
    K. Symanzik, DESY preprint 77/05Google Scholar
  35. 35.
    A.A. Migdal, Sov.Phys. JEPT 28 (1969) 1036ADSGoogle Scholar
  36. 36.
    A.M. Poliakov, Sov.Phys. JEPT 20 (1969) 533ADSGoogle Scholar
  37. 37.
    A.M. Poliakov, JEPT Letters 12 (1970) 381ADSGoogle Scholar
  38. 38.
    G. Parisi, L. Peliti, Lett.Nuov. Cimento 2 (1971) 627, Phys.Lett. 41A (1972) 331CrossRefGoogle Scholar
  39. 39.
    G. Nack, L. Todorov, Phys.Rev. D8 (1973) 1764CrossRefGoogle Scholar
  40. 40.
    C. Callan, R. Dashen, D. Gross, Phys.Lett. 63B (1976) 334CrossRefGoogle Scholar
  41. 41.
    R. Jackiw, C. Rebbi, Phys.Rev.Lett. 37 (1976) 172ADSCrossRefGoogle Scholar
  42. 42.
    K. Symanzik, Nuovo.Cim.Lett. 6 (1973) 420CrossRefGoogle Scholar
  43. 43.
    G. ’t Hooft, Marseille Conference June 1972 (unpublished)Google Scholar
  44. 44.
    H.D. Politzer, Phys.Rev.Lett. 30 (1973) 1346ADSCrossRefGoogle Scholar
  45. 45.
    D.J. Gross, F. Wilczek, Phys.Rev.Lett. 30 (1973) 1343ADSCrossRefGoogle Scholar
  46. 46.
    E. Brezin, J. Zinn-Justin, Phys.Rev. 36 (1976) 691ADSGoogle Scholar
  47. 47.
    R. Balian, C. Bloch, Annals of Phys. 85 (1974) 514ADSCrossRefzbMATHMathSciNetGoogle Scholar
  48. 48.
    K.G. Wilson, J. Kogut, Phys.Reports 12C (1974) 75ADSCrossRefGoogle Scholar
  49. 49.
    C.A. Baker, B.C. Nikel, M.S. Green, D.I. Meiron, Phys.Rev. Lett. 36 (1976) 1351.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • G. Parisi
    • 1
  1. 1.Laboratoire de Physique Théorique de l’Ecole Normale SupérieureParis Cedex 05France

Personalised recommendations