Valley views: instantons, large order behaviors, and supersymmetry
Valley views: instantons, large order behaviors, and supersymmetry
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谷观点：瞬子、大阶行为和超对称性
DOI：
10.1016/s0550-3213(99)00263-1
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Shinya Wada
中科院分区：
文献类型：
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作者：
H. Aoyama;H. Kikuchi;Ikuo Okouchi;Masatoshi Sato;Shinya Wada
对拓扑平凡扇区中瞬子性质的解释一直是一个长期的难题。在这里，我们声称，性质可以概括的几何结构的配置空间，谷。这一主张的证据是以各种方式提出的。统一了常规微扰理论和非微扰计算，消除了微扰级数的Borel变换的模糊性。Bogomolny的“技巧”的“证明”，这使我们能够超越稀气体近似。微扰理论的预测的大阶行为证实了明确的计算，在某些情况下，到478阶。一种新的类型的超对称性被发现作为一个副产品，我们的结果是一致的非重整化定理。用薛定谔方程的数值解证实了能级的预测。
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. Evidence for this claim is presented in various ways. The conventional perturbation theory and the non-perturbatioe 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 perturbation theory is confirmed by explicit calculations, in some cases to the 478th 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 Schrödinger equation.