Non-perturbative Analysis of Field Theories by Renormalization Group

重正化群对场论的非微扰分析

• 批准号: 08640361
• 负责人: TERAO Haruhiko
• 金额: $ 1.34万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640361/
• 关键词: Renormlization group; Non-perturbative analysis; Chiral symmetry; Phase transition; Supersymmetry; 場の量子論; 非摂動; くりこみ群; 対称性の自発的破れ; ゲージ理論; シュウインガー・ダイソン方程式; はしご近似; ゲージ不変性

Non-perturbative dynamics of held theories has been one of the most important subject in particle physics. However we cannot help but saying that the present non-perturbative analytic methods are still in a rather poor level. We tried to develop the non-perturbative (exact) renormalization group (RG) as such a general method. We studied the formulation of the RG equations and the effective scheme of approximnation. Also we first have applied the non-perturbative RO to dynamical chiral symmetry breaking, which is quite significant phenomena in particle physics to be clarified, and developed the scheme of analysis. The non-perturbative phenomena like instanton effects have also analyzed through the non-perturbative RG method by studying the quantum mechanical models. As by-products, it has been found that the RG method is able to capture the famous spontaneous supersymmetry breaking.On the other hand we studied the non-perturbative dynamics in supersymmetric gauge thories. Especially we have clarified the several physical properties of N=2 supersymmetric QCD vacua ; symmetry breaking, CP symmetry, theta angle dependence, charges of dyons and so on.

理论的非微扰动力学一直是粒子物理学中最重要的课题之一。但我们不能不说，目前的非微扰分析方法还处于相当差的水平。我们尝试开发非微扰（精确）重正化群（RG）作为这样一种通用方法。我们研究了RG方程的表述和有效的逼近方案。我们还首次将非微扰RO应用于动态手性对称性破缺，这是粒子物理学中非常重要的现象，有待澄清，并制定了分析方案。通过研究量子力学模型，还通过非微扰RG方法对瞬子效应等非微扰现象进行了分析。作为副产品，人们发现RG方法能够捕获著名的自发超对称破缺。另一方面，我们研究了超对称规范理论中的非微扰动力学。特别是阐明了N=2超对称QCD真空的几个物理性质；对称性破缺、CP 对称性、theta 角依赖性、dyon 电荷等。

项目成果

K.Konishi: "CP,Charge fractionalization and low energy effective actions in the SU(2) Seiberg-Witten theories with quarks" Nuclear Physics. B511. 264-294 (1998)

K.Konishi：“夸克 SU(2) Seiberg-Witten 理论中的 CP、电荷分裂和低能有效作用”核物理。

K.-I.Aoki: "Non-perturbative Renormalization Group Analysis of the Chiral Critical Behavior in QED" Progress of Theore tical Physics. 97 No.3. 479-489 (1997)

K.-I.Aoki：“QED 中手征临界行为的非微扰重正化群分析”理论物理进展。

K-I.Aoki, K.Horikawa, W.Souma, J.Sumi, H.Terao: "Rapidly Converging Truncation Scheme of the Exact Renormalization Group" Progress of Theoretical Physics. 99(to be published). (1988)

K-I.Aoki、K.Horikawa、W.Souma、J.Sumi、H.Terao：“精确重正化群的快速收敛截断方案”理论物理进展。

K.-I.Aoki: "Rocpialy Converging Truncation scleme of the Exact Renomalization Group" Progress of Theoretical Physics. 99 No.31. 451-466 (1998)

K.-I.Aoki：“精确重整群的 Rocpialy 收敛截断方案”理论物理进展。

K.Konishi: "CD.Charge fractionalitations and low energy effective octions in the SU(2) Seiberg-Witter tleories with quarks" Nuclear Physics. B511. 264-294 (1998)

K.Konishi：“夸克 SU(2) Seiberg-Witter 理论中的 CD.电荷分馏和低能有效作用”核物理。