Feynman diagrams and large order estimates for the exponential anharmonic oscillator

Stephen Breen

Annales de l'I.H.P. Physique théorique (1987)

  • Volume: 46, Issue: 2, page 155-173
  • ISSN: 0246-0211

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Breen, Stephen. "Feynman diagrams and large order estimates for the exponential anharmonic oscillator." Annales de l'I.H.P. Physique théorique 46.2 (1987): 155-173. <http://eudml.org/doc/76355>.

@article{Breen1987,
author = {Breen, Stephen},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {functional integration; perturbation coefficients; exponential anharmonic oscillator; Feynman diagram representations; path integral estimates},
language = {eng},
number = {2},
pages = {155-173},
publisher = {Gauthier-Villars},
title = {Feynman diagrams and large order estimates for the exponential anharmonic oscillator},
url = {http://eudml.org/doc/76355},
volume = {46},
year = {1987},
}

TY - JOUR
AU - Breen, Stephen
TI - Feynman diagrams and large order estimates for the exponential anharmonic oscillator
JO - Annales de l'I.H.P. Physique théorique
PY - 1987
PB - Gauthier-Villars
VL - 46
IS - 2
SP - 155
EP - 173
LA - eng
KW - functional integration; perturbation coefficients; exponential anharmonic oscillator; Feynman diagram representations; path integral estimates
UR - http://eudml.org/doc/76355
ER -

References

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  3. [3] E. Caliceti, V. Grecchi, S. Levoni and M. Maioli, The exponential anharmonic oscillator and the Stieltjes continued fraction, preprint. Zbl0581.34020MR784297
  4. [4] M. Maioli, Exponential perturbations of the harmonic oscillator. J. Math. Phys., t. 22, 1981, p. 1952-1958. Zbl0472.47025MR631146
  5. [5] A. Sokal, An improvement of Watson's theorem on Borel summability. J. Math. Phys., t. 21, 1980, p. 261-263. Zbl0441.40012MR558468
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  8. [8] S. Breen, Leading large order asymptotics for (φ4)2 perturbation theory. Commun. Math. Phys., t. 92, 1983, p. 179-194. Zbl0568.46055MR728864
  9. [9] S. Breen, Large order perturbation theory for the anharmonic oscillator. Mem. Amer. Math. Soc., to appear. Zbl0623.28010
  10. [10] J. Magnen and V. Rivasseau, The Lipatov argument for φ43 perturbation theory. Commun. Math. Phys., t. 102, 1985, p. 59-88. MR817288
  11. [11] A. Dolgov and V. Popov, Modified perturbation theories for an anharmonic oscillator. Phys. Lett., B., t. 79, 1978, p. 403-405. 
  12. [12] B. Simon, Functional integration and quantum physics, New York. Academic Press, 1979. Zbl0434.28013MR544188
  13. [13] B. Simon, The P (φ)2 Euclidean (quantum) field theory. Princeton, Princeton University Press, 1974. MR489552
  14. [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. MR441150
  15. [15] B. Simon, Large orders and summability of eigenvalue perturbation theory: a mathematical overview. Int. J. Q. Chem., t. 21, 1982, p. 3-25. 

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