Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-08-06
Nucl.Phys. B553 (1999) 644-710
Physics
High Energy Physics
High Energy Physics - Theory
78 pages, Latex, 22 eps figures
Scientific paper
10.1016/S0550-3213(99)00263-1
The elucidation of the properties of the instantons in the topologically trivial sector has been a long-standing puzzle. Here we claim that the properties can be summarized in terms of the geometrical structure in the configuration space, the valley. The evidence for this claim is presented in various ways. The conventional perturbation theory and the non-perturbative calculation are unified, and the ambiguity of the Borel transform of the perturbation series is removed. A `proof' of Bogomolny's ``trick'' is presented, which enables us to go beyond the dilute-gas approximation. The prediction of the large order behavior of the perturbation theory is confirmed by explicit calculations, in some cases to the 478-th order. A new type of supersymmetry is found as a by-product, and our result is shown to be consistent with the non-renormalization theorem. The prediction of the energy levels is confirmed with numerical solutions of the Schr\"{o}dinger equation.
Aoyama Hideaki
Kikuchi Hisashi
Okouchi Ikuo
Sato* Masatoshi
Wada Shinya
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