Non Perturbative Dimensional Interpolation

V. Rivasseau; A. S. Wightman

Recherche Coopérative sur Programme n°25 (1980)

  • Volume: 28, page 0-41

How to cite


Rivasseau, V., and Wightman, A. S.. "Non Perturbative Dimensional Interpolation." Recherche Coopérative sur Programme n°25 28 (1980): 0-41. <>.

author = {Rivasseau, V., Wightman, A. S.},
journal = {Recherche Coopérative sur Programme n°25},
language = {fre},
pages = {0-41},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Non Perturbative Dimensional Interpolation},
url = {},
volume = {28},
year = {1980},

AU - Rivasseau, V.
AU - Wightman, A. S.
TI - Non Perturbative Dimensional Interpolation
JO - Recherche Coopérative sur Programme n°25
PY - 1980
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 28
SP - 0
EP - 41
LA - fre
UR -
ER -


  1. [1] N. N. Khuri, Zeros of the Gell-Mann-Low function and Borel summations in the renormalizable theories ; The slope of the Gell-Mann-Low function at the U.V. fixed point. Rockefeller University preprints, 1979. 
  2. [2] D. Marchesin, The Scaling limit of the φ 2 field in the anharmonic oscillator : existence and numerical studies, Rockefeller University preprint 1978. MR531285
  3. [3] J. Glimm, A. Jaffe, Absolute bounds on vertices and couplings ; On the approach to the cirtical point, Ann. Inst. H. Poincaré, 22, 1975 pp. 97-122. MR384012
  4. [4] J. Magnen, R. Sénéor, Phase Space Cell Expansion and Borel Summability for the Euclidean φ 3 4 Theory, Commun. Math. Phys.56, 1977, pp 237-276. MR523030
  5. [5] A. Sokal, An improvement of Watson's theorem on Borel summability, Princeton University preprint, 1979. Zbl0441.40012
  6. [6] E. Speer, Dimensional and Analytic Renormalization, in "Renormalization Theory", edited by G. Velo and A.S. Wightman, D. Reidel Publishing Company, Dordrecht, Holland, 1976, pp 25-93. MR522287
  7. [7] Nous remercions Monsieur H. Epstein, qui nous a signalé l'importance de ce point. 
  8. [8] M. C. Bergère, J. B. Zuber, Renormalization of Feynman Amplitudes and Parametric Integral Representation, Commun. Math. Phys.35, 1974, pp 113-140. MR342090
  9. M. C. Bergère, Y. M. P. Lam, Bogoliubov-Parasiuk, Theorem in the α-parametric representation, Jour. Math. Phys.17, 1976, pp 1546-1557. MR424068
  10. [9] M. C. Bergère, F. David, communication privée. 
  11. [10] J. P. Eckmann, A. Sokal, communications privées. 
  12. [11] C. M. Bender, T.-T. Wu, Anharmonic oscillator, Phys. Rev.184, No. 5, 1969 p. 1231. MR260323
  13. Voir aussi Bender, Lin : Tight lower and upper bounds for the anharmonic oscillator, preprint 1979. 
  14. [12] B. Simon, communication privée, et Functional Integration and Quantum Physics, Cours donné à Lausanne, 1977. Zbl1061.28010
  15. [13] J. Glimm, Boson fields with the : φ 4 : interaction in three dimensions, Commun. Math. Phys.10, 1968, pp 1-47. Zbl0175.24702MR231601
  16. [14] V. Rivasseau, Sommation et estimations d'amplitudes de Feynman, Thèse de 3° cycle, Université Paris VI, 1979. 
  17. [15] J. P. Eckmann, H. Epstein, J. Fröhlich, Asymptotic perturbation expansion for the S-matrix and the definition of the time-ordered functions in relativistic quantum field models, Ann. Inst. H. Poincaré, 25, 1976, pp 1-34. MR418716
  18. J. P. Eckmann, H. Epstein, Borel summability of the mass and the S-matrix in φ 4 models, I.H.E.S. preprint, 1979. MR544880

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