Analyticity and Borel summability of the φ 4 models. I. The dimension d = 1

Claude Billionnet; Pierre Renouard

Annales de l'I.H.P. Physique théorique (1993)

  • Volume: 59, Issue: 2, page 141-199
  • ISSN: 0246-0211

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Billionnet, Claude, and Renouard, Pierre. "Analyticity and Borel summability of the $\phi ^4$ models. I. The dimension $d = 1$." Annales de l'I.H.P. Physique théorique 59.2 (1993): 141-199. <http://eudml.org/doc/76619>.

@article{Billionnet1993,
author = {Billionnet, Claude, Renouard, Pierre},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Schwinger functions of the models; analytic functions of the coupling constant},
language = {eng},
number = {2},
pages = {141-199},
publisher = {Gauthier-Villars},
title = {Analyticity and Borel summability of the $\phi ^4$ models. I. The dimension $d = 1$},
url = {http://eudml.org/doc/76619},
volume = {59},
year = {1993},
}

TY - JOUR
AU - Billionnet, Claude
AU - Renouard, Pierre
TI - Analyticity and Borel summability of the $\phi ^4$ models. I. The dimension $d = 1$
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 59
IS - 2
SP - 141
EP - 199
LA - eng
KW - Schwinger functions of the models; analytic functions of the coupling constant
UR - http://eudml.org/doc/76619
ER -

References

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  1. [1] C. Billionnet and P. Renouard, Analytic Interpolation and Borel Summability of the (λ/N|φN|:4)2 Models, I. Finite Volume Approximation, C.M.P., Vol. 84, 1982, pp. 257-295. MR661137
  2. [2] M. Duneau, D. Iagolnitzer and B. Souillard, Strong Cluster Properties for Classical Systems with Finite Range Interactions, C.M.P., Vol. 35, 1974, pp. 307-320. MR337230
  3. [3] J.P. Eckmann, J. Magnen and R. Seneor, Decay Properties and Borel Summability for the Schwinger Functions in P (φ)2 Theories, CMP, Vol. 39, 1975, pp. 251-271. MR366266
  4. [4] J. Glimm, A. Jaffe and T. Spencer, The Particle Structure of the Weakly Coupled P(φ)2 Model... Part II. The Cluster Expansion, Lecture Notes in Physics, Springer, Vol. 25, 1973, pp. 199-242. MR395513
  5. [5] J. Glimm and A. Jaffe, Positivity of the φ43 Hamiltonian, Fortschritte der Physik, Vol. 21, 1973, pp. 327-376. MR408581
  6. [6] F. Guerra, L. Rosen and B. Simon, The P(φ)2 Euclidean Quantum Field Theory as Classical Statistical Mechanics, Ann. Math., Vol. 101, 1975, p. 111. MR378670
  7. [7] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. Zbl0148.12601
  8. [8] N. Khuri, Stability of Asymptotically Free Φ44, 1984. 
  9. [9] J. Magnen and R. Seneor, The Infinite Volume Limit of the φ43 Model, Ann. I.H.P., Vol. 24, 1976, pp. 95-159. MR406217
  10. [10] E. Nelson, The Free Markov Field, J. Funct. Anal., Vol. 12, 1973, p. 211. Zbl0273.60079MR343816
  11. [11] P. Renouard, Analyticité et sommabilité de Borel des fonctions de Schwinger du modèle de Yukawa en dimension d=2, II. La « limite adiabatique », Ann. I.H.P., Vol. 31, 1979, pp. 235-318. MR571894
  12. [12] B. Simon, Coupling Constant Analyticity for the Anharmonic Oscillator, Ann. of Physics, Vol. 58, 1970, pp. 76-136. MR416322
  13. [13] B. Simon, Notes on Infinite Determinants of Hilbert Space Operators, Zbl0353.47008
  14. [14] T. Spencer, The Decay of the Bethe-Salpeter Kernel in P(φ)2 Quantum Field Models, CMP, Vol. 44, 1975, pp. 143-164. MR389080
  15. [15] T. Spencer, The Lipatov Argument, C.M.P., Vol. 74, 1980, pp. 273-280. MR578044
  16. [16] H. Triebel, Theory of Function Spaces, Monographs in Mathematics, Birkhäuser, Vol. 78, 1983. Zbl0546.46027MR730762
  17. [17] A. Wightman, Φ4v and Generalized Borel Summability, Canadian Math. Soc. Conference Proceedings, Vol. 9, 1988, pp. 1-13. MR973453

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