Macroscopic Variables and Hilbert C^*-Modules in Algebraic Quantum Field Theory

代数量子场论中的宏观变量和希尔伯特 C^* 模

• 批准号: 11640113
• 负责人: OJIMA Izumi
• 金额: $ 1.54万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640113/
• 关键词: Spontaneous symmetry breaking; Tannaka-Krein duality; Algebraic quantum field theory; C^*-category; Homotopy; Induced representations; Superselction theory; Order parameters; 超対称性; de Rhamカレント; 超伝導; Josephson効果; 対称性の破れ

In 1999 together with Prof. Maumary (Univ. de Lausanne, Switzerland) I clarified deep connections between supersymmetry and homotopy formulated in an algebraic and categorical form (S.Maumary and I.Ojima, "Supersymmetry and Homotopy" which is now under revision). Along the general formulation of macroscopic variables arising from spontaneous symmetry breaking (SSB), I investigated the Josephson effect as the most important ingredient in superconductivity : In contrast to the traditional derivation whose general validity is unclear, I succeeded in obtaining a concise derivation of the Josephson formulae which clarifies the essence of Josephson current as the physical effect due to the difference in order parameters accross two adjacent phases. In close connection with this theme, I have continued the research on the general formulation of local temperature states in algebraic QFT together with Profs.D.Buchholz, H.Roos in Germany (to be completed by the coming summer) and on the generali … More zation of superselction theory to SSB cases the latter of which constitutes the main contents of my research in 2000.Regarding the later, I have worked on mathematical preparations for it : In contrast to Tannaka-Krein duality for compact groups playing the essential roles in the cases of unbroken symmetry, the extension of duality to homogeneous spaces becomes important in our case of SSB.What I obtained with Prof. Maumary is a result for this extension in use of the homotopy-fiber category, on the basis of which the research has been going on. To completie the project, we need to combine this result with a method which allows the extension of the algebra with unbroken subgroup symmetry to a larger one with full symmetry. For this purpose, the investigation on Goldstone multiplets, order parameters and the centres of represented algebras done in preparation for my series lectures "Thermal Instability of Supersymmetry I, II") at Borel Seminar 2000 is expected to play important roles. Along these lines, the project is expected to be completed this year. Less

1999年，我和瑞士洛桑大学的Maumary教授一起阐明了超对称性和以代数和范畴形式表述的同伦之间的深刻联系（S.Maumary和I.Ojima，“Supersymmetry and Homotopy”，目前正在修订中）。沿着由自发对称破缺（SSB）产生的宏观变量的一般公式，我研究了约瑟夫森效应作为超导性中最重要的成分：与一般有效性不明确的传统推导相反，本文成功地得到了约瑟夫森公式的简明推导，阐明了约瑟夫森电流的本质是由于不同的阶参数引起的物理效应。两个相邻的阶段。与此密切相关，我与德国的D.布赫霍尔茨、H.鲁什教授一起继续研究了代数量子场论中局域温度态的一般形式（将于今年夏天完成）， ...更多信息 超选择理论在单边带情形下的应用，后者是我2000年研究的主要内容。与紧致群的Tannaka-Krein对偶相反，紧致群在对称性不破缺的情况下扮演着重要角色，对偶到齐性空间的推广在我们的SSB情形中变得重要。我和Maumary教授一起得到的是利用同伦纤维范畴对这种推广的一个结果，在此基础上，我们进行了进一步的研究，为了完成这一课题，我们需要将这一结果与一种方法相结合，这种方法允许将具有不破开子群对称性的代数推广到一个更大的具有全对称性的代数。为此目的，调查戈德斯通多重态，序参数和中心所代表的代数做准备我的系列讲座“热不稳定性的超对称I，II”）在Borel研讨会2000年预计将发挥重要作用。沿着这些路线，该项目预计将在今年完成。少

项目成果

小嶋泉: "Towards Local Temperature States in QFT"京大数理研講究録「量子情報と量子カオスの数理」. 1142. 123-136 (2000)

小岛泉：“走向 QFT 中的局域温度状态”京都大学数学研究所讲座“量子信息和量子混沌的数学”1142. 123-136 (2000)。

Izumi Ojima: "A Simple Derivation of Josephson Formulae in Superconductivity"Lett.Math.Phys.. 51. 257-264 (2000)

小岛泉：“超导性约瑟夫森公式的简单推导”Lett.Math.Phys.. 51. 257-264 (2000)

Izumi Ojima: "Spontaneous Collapse of supersymmetry"in Proc. 2nd Jagna Intern. Workshop on "Mathematical Methods of Quantum Physics" eds. C.C.Bernido, et al., (Gordon Breach). 275-286 (1999)

小岛泉：“超对称性的自发塌缩”，Proc。

Izumi Ojima: "A Simple Derivation of Josephson Formulae in Superconductivity"to appear in Lett.Math.Phys.. (2000)

小岛泉：“超导约瑟夫森公式的简单推导”出现在 Lett.Math.Phys.. (2000)