Abstract
Unlike the ε=0 case, the perturbation series of the unequal double wellp 2+x 2+2gx 3+g 2(1+ε)x 4 are Borel summable to the eigenvalues for any ε>0.
Similar content being viewed by others
References
Coleman, S.: The uses of instantons. Proceedings Intern. School of Physics, Erice 1977
Gildener, E., Patrasciou, A.: Pseudoparticle contributions to the energy spectrum of a one-dimensional system. Phys. Rev. D16, 423–433 (1977)
Graffi, S., Grecchi, V.: The Borel sum of the double-well perturbation series and the Zinn-Justin conjecture. Phys. Lett.121 B, 410 (1983)
Hellwig, G.: Differentialoperatoren der mathematischen Physik. Berlin, Heidelberg, New York: Springer 1964
Herbst, I., Simon, B.: Some remarkable examples in eigenvalue perturbation theory. Phys. Lett.78 B, 304 (1978)
't Hooft, G.: Borel summability of a four-dimensional field theory. Phys. Lett.119 B, 369 (1982)
't Hooft, G.: Is asymptotic freedom enough? Phys. Lett.109 B, 474 (1982)
Hunziker, W., Vock, E.: Stability of Schrödinger eigenvalue problems. Commun. Math. Phys.83, 208 (1982)
Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966
Sibuya, Y.: Global theory of a second order differential equation with a polynomial coefficient. Amsterdam: North-Holland 1975
Simon, B.: Instantons, double-wells, and large deviations. California Institute of Technology (preprint)
Simon, B.: Coupling constant analyticity for the anharmonic oscillator. Ann. Phys.58, 76 (1970)
Reed, M., Simon, B.: Methods of modern mathematical physics. IV. Analysis of operators. New York: Academic Press 1978
Sokal, A.: An improvement of Watson's theorem on Borel summability. J. Math. Phys.21, 261 (1980)
Author information
Authors and Affiliations
Additional information
Communicated by B. Simon
Rights and permissions
About this article
Cite this article
Graffi, S., Grecchi, V. Borel summability of the unequal double well. Commun.Math. Phys. 92, 397–403 (1984). https://doi.org/10.1007/BF01210728
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01210728