Feynman diagrams and large order estimates for the exponential anharmonic oscillator
Annales de l'I.H.P. Physique théorique, Volume 46 (1987) no. 2, p. 155-173
@article{AIHPA_1987__46_2_155_0,
     author = {Breen, Stephen},
     title = {Feynman diagrams and large order estimates for the exponential anharmonic oscillator},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {2},
     year = {1987},
     pages = {155-173},
     zbl = {0623.28010},
     mrnumber = {887145},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1987__46_2_155_0}
}
Breen, Stephen. Feynman diagrams and large order estimates for the exponential anharmonic oscillator. Annales de l'I.H.P. Physique théorique, Volume 46 (1987) no. 2, pp. 155-173. http://www.numdam.org/item/AIHPA_1987__46_2_155_0/

[1] V. Grecchi and M. Maioli, Borel summability beyond the factorial growth. Ann. Inst. H. Poincaré, Sect. A., t. 41, 1984, p. 37. | Numdam | MR 760125 | Zbl 0551.40009

[2] V. Grecchi and M. Maioli, Generalized logarithmic Borel summability. J. Math. Phys., t. 25, 1984, p. 3439-3443. | MR 767548 | Zbl 0562.40006

[3] E. Caliceti, V. Grecchi, S. Levoni and M. Maioli, The exponential anharmonic oscillator and the Stieltjes continued fraction, preprint. | MR 784297

[4] M. Maioli, Exponential perturbations of the harmonic oscillator. J. Math. Phys., t. 22, 1981, p. 1952-1958. | MR 631146 | Zbl 0472.47025

[5] A. Sokal, An improvement of Watson's theorem on Borel summability. J. Math. Phys., t. 21, 1980, p. 261-263. | MR 558468 | Zbl 0441.40012

[6] M. Reed and B. Simon, Methods of modern mathematical physics. Vol. IV, New York, Academic Press, 1975. | Zbl 0401.47001

[7] T. Spencer, The Lipatov argument. Commun. Math. Phys., t. 74, 1980, p. 273-280. | MR 578044

[8] S. Breen, Leading large order asymptotics for (φ4)2 perturbation theory. Commun. Math. Phys., t. 92, 1983, p. 179-194. | MR 728864 | Zbl 0568.46055

[9] S. Breen, Large order perturbation theory for the anharmonic oscillator. Mem. Amer. Math. Soc., to appear.

[10] J. Magnen and V. Rivasseau, The Lipatov argument for φ43 perturbation theory. Commun. Math. Phys., t. 102, 1985, p. 59-88. | MR 817288

[11] A. Dolgov and V. Popov, Modified perturbation theories for an anharmonic oscillator. Phys. Lett., B., t. 79, 1978, p. 403-405.

[12] B. Simon, Functional integration and quantum physics, New York. Academic Press, 1979. | MR 544188 | Zbl 0434.28013

[13] B. Simon, The P (φ)2 Euclidean (quantum) field theory. Princeton, Princeton University Press, 1974. | MR 489552

[14] F. Guerra, L. Rosen, and B. Simon, Boundary conditions in the P(φ)2 Euclidean field theory. Ann. Inst. H. Poincaré, Sect. A, t. 25, 1976, p. 231-334. | Numdam | MR 441150

[15] B. Simon, Large orders and summability of eigenvalue perturbation theory: a mathematical overview. Int. J. Q. Chem., t. 21, 1982, p. 3-25.