Tunnel Effects in Field Theory and Asymptotic Behavior of Perturbation Theories

场论中的隧道效应和微扰理论的渐近行为

• 批准号: 07640391
• 负责人: AOYAMA Hideaki
• 金额: $ 1.28万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640391/
• 关键词: Tunnel Effects; Perturbation Theory; Valley Method; Non-Perturbative Effects; Instanton; Bounce; Asymptotic Series; Field Theory; バレー・メソッド; 固有谷法; 経路積分法; 超対称性; アシンプトン; 非摂動的効果

This year, we made progress in the analysis of the structure of the quantum theories using the valley method. The imaginary-time path-integral method is known to be effective for the treatment of the tunneling phenomena. The well-known calculation utilizing instanton or bounce solutions, however, have various limitations. In order to overcome those, the team involving the present investigator has established the "valley method".The one-dimensional asymmetric double-well potential model has been analyzed in detail this year, to yield the following results :・The non-perturbative effects due to the tunneling can be incorporated by use of valley-instanton and valley-bounces.・This effect can be completely separated from perturbative effect by an analytic continuation of the valley parameter. This analytic continuation at the same time allows calculation by using only the leading contribution of the interactions of the valley-instantons.・This analysis shows that the singularity in the valley integration leads to the evaluation of the leading term of the non-Borcl-summable divergence in perturbation series. This result differs from a widely known folklore.・Our prediction for the asymptotic behavior of the perturbative series has been confirmed to the 300-th order by direct algebraic calculation.We believe that these results lead to a knowledge of the general relation between the perturbative and non-perturbative effects in quantum theories.

今年，我们在使用谷方法分析量子理论的结构方面取得了进展。时间路径积分法是处理隧道效应的有效方法。然而，利用瞬子或反弹解的公知计算具有各种限制。为了克服这些问题，本研究小组建立了“谷方法”，今年对一维非对称双阱势模型进行了详细分析，得到了以下结果：·利用谷瞬子和谷反弹，可以将隧道效应引起的非微扰效应考虑在内。·这种效应可以通过谷参数的解析延拓而与微扰效应完全分离。这种解析延拓同时允许只使用谷瞬子相互作用的主导贡献进行计算。·这一分析表明，在谷积分的奇异性导致的非Borcl可和的发散扰动系列的领导项的评估。这一结果与广为人知的民间传说不同。·我们对微扰级数渐近行为的预言已被直接代数计算证实到300阶，我们相信这些结果有助于了解量子理论中微扰效应和非微扰效应之间的一般关系。

项目成果

H. Aoyama: "Recent Developments in the Theory of Quantum Tunneling" Proc. of the 4th Haergdang Summer Wurtshop. section-7. 1-20 (1995)

H. Aoyama：“量子隧道理论的最新进展”Proc。

H.Aoyama, T.Harano, M.Sato, and S.Wada: "Valley Instanton in the Gauge-Higgs System" Mod.Phys.Lett.All. 43-54 (1996)

H.Aoyama、T.Harano、M.Sato 和 S.Wada：“规范希格斯系统中的谷瞬子”Mod.Phys.Lett.All。

H.Aoyama, H.Kikuchi, I.Okouchi, M.Sato, and S.Wada: "Valleys in Quantum Mechanics" Phys.Lett. B (in press). (1998)

H.Aoyama、H.Kikuchi、I.Okouchi、M.Sato 和 S.Wada：“量子力学中的谷”Phys.Lett。

H. Aoyama, T. Haravo M. Sato, S. Woda: "Valley Instanton in the Gauge-Higgs System" Mod Phys. Lett. A. (発表予定). (1996)

H. Aoyama、T. Haravo M. Sato、S. Woda：“规范希格斯系统中的谷瞬子”Mod Phys A.（即将出版）。

H.Aoyama, T.Harano, M.Sato, and S.Wada: "Valley Instanton versus Constrained Instanton" Nucl.Phys.B466. 127-158 (1996)

H.Aoyama、T.Harano、M.Sato 和 S.Wada：“谷瞬时子与约束瞬时子”Nucl.Phys.B466。