Non Perturbative Dimensional Interpolation

Rivasseau, V.; Wightman, A. S.

Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 28 (1980), p. 0-41 / Harvested from Numdam

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Publié le : 1980-01-01

@article{RCP25_1980__28__0_0,
     author = {Rivasseau, V. and Wightman, A. S.},
     title = {Non Perturbative Dimensional Interpolation},
     journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
     volume = {28},
     year = {1980},
     pages = {0-41},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/RCP25_1980__28__0_0}
}

Rivasseau, V.; Wightman, A. S. Non Perturbative Dimensional Interpolation. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 28 (1980) pp. 0-41. http://gdmltest.u-ga.fr/item/RCP25_1980__28__0_0/

Bibliographie

[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] D. Marchesin, The Scaling limit of the $φ^{2}$ field in the anharmonic oscillator : existence and numerical studies, Rockefeller University preprint 1978. | MR 531285

[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. | Numdam | MR 384012

[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. | MR 523030

[5] A. Sokal, An improvement of Watson's theorem on Borel summability, Princeton University preprint, 1979. | Zbl 0441.40012

[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. | MR 522287

[7] Nous remercions Monsieur H. Epstein, qui nous a signalé l'importance de ce point.

[8] M. C. Bergère, J. B. Zuber, Renormalization of Feynman Amplitudes and Parametric Integral Representation, Commun. Math. Phys. 35, 1974, pp 113-140. | MR 342090

M. C. Bergère, Y. M. P. Lam, Bogoliubov-Parasiuk, Theorem in the $α$ -parametric representation, Jour. Math. Phys. 17, 1976, pp 1546-1557. | MR 424068

[9] M. C. Bergère, F. David, communication privée.

[10] J. P. Eckmann, A. Sokal, communications privées.

[11] C. M. Bender, T.-T. Wu, Anharmonic oscillator, Phys. Rev. 184, No. 5, 1969 p. 1231. | MR 260323

Voir aussi Bender, Lin : Tight lower and upper bounds for the anharmonic oscillator, preprint 1979.

[12] B. Simon, communication privée, et Functional Integration and Quantum Physics, Cours donné à Lausanne, 1977. | Zbl 1061.28010

[13] J. Glimm, Boson fields with the $: φ^{4} :$ interaction in three dimensions, Commun. Math. Phys. 10, 1968, pp 1-47. | MR 231601 | Zbl 0175.24702

[14] V. Rivasseau, Sommation et estimations d'amplitudes de Feynman, Thèse de 3° cycle, Université Paris VI, 1979.

[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. | Numdam | MR 418716

J. P. Eckmann, H. Epstein, Borel summability of the mass and the S-matrix in $φ^{4}$ models, I.H.E.S. preprint, 1979. | MR 544880