Instantons in Quantum Mechanics and Resurgent Expansions

Details Instantons in Quantum Mechanics and Resurgent Expansions Instantons in Quantum Mechanics and Resurgent Expansions

2004-05-27

arxiv.org/abs/hep-ph/0405279v3

Phys.Lett.B596:138-144,2004

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, LaTeX; further typographical errors corrected

Scientific paper

10.1016/j.physletb.2004.06.077

Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical case, the eigenvalue may be expressed in terms of a generalized perturbative expansion (resurgent expansion). Modified Bohr-Sommerfeld quantization conditions lead to generalized perturbative expansions which may be expressed in terms of nonanalytic factors of the form exp(-a/g), where a > 0 is the instanton action, and power series in the coupling g, as well as logarithmic factors. The ground-state energy, for the specific Hamiltonians, is shown to be dominated by instanton effects, and we provide numerical evidence for the validity of the related conjectures.

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