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结构方面取得了进展，众所周知，虚数时间路径积分方法对于处理隧道现象非常有效。然而，弹跳解决方案具有各种局限性，为了克服这些局限性，本研究人员的团队建立了“谷法”。今年对一维不对称双阱电势模型进行了详细分析，得出了以下结果：・可以通过使用谷瞬时和谷反弹来合并由隧道效应引起的非扰动效应。 ・通过谷参数的解析延拓，可以将该效应与扰动效应完全分离。该解析延拓同时允许计算。仅使用谷瞬时相互作用的主导贡献。・该分析表明，谷积分中的奇异性导致了对非 Borcl 可求和散度的主导项的评估这个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测已通过直接代数计算得到了第 300 阶的证实。我们相信这些结果导致了对一般关系的了解。量子理论中的微扰效应和非微扰效应之间的关系。

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. 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, 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.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, 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。