Systems with Spontaneously Broken Symmetries and Nonperturbative Methods

对称性自发破缺的系统和非微扰方法

• 批准号: 13135217
• 负责人: KASHIWA Taro
• 金额: $ 12.99万
• 依托单位: Ehime University (2002-2006)Kyushu University (2001)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13135217/
• 关键词: Path Integration; Auxiliary Fields Methods; Theta Terms; Maximal Entropy Methods; Higher Derivative Gravity; Higher Dimensional Spacetime; Grand Unified Theories; Anomalous U (1) Theory; 高階微分; データ項; 繰り込み群; オービフィールド; 3核子力; ブレイン宇宙; 量子情報; 南部-J

In this project, the head investigator Taro Kashiwa studied the validity of the Auxiliary Field Method(AFM) in the cases of 0-and 1-dimensional Bosonic and Fermionic models. In 0-deminional cases, it was found that in the huge range of the coupling constant the 1-loop results fit well with the exact value, and that there arises the caustics, characterized by the vanishing of the second derivative of the action in the exponent under path integrals, in the 0-dimensiona four-fermi model. The 1-dimensional bosnic case (Quantum Mecanical case) with the double well potential needs higher loop corrections in the region where the instantons play an important role, which would be cured by the introduction of additional auxiliary fileds. This is now under investigation.Yasuo Ezawa studied the gravity theories containing higher derivatives; they found the issue, the Hamiltonian in the Buchbinder-Lyakhovich (BL) canonical formalism must be transformed under the general coordinate transformation, is resolved by the combination of BL with Ostrogradski formalism.Yoshiharu Kawamura found the grand unified models in the 5-dimensional spacetime which can explain the origin of the generation and the sum rule for masses of constituent particles in the case of the supersymmetric extension of those models. The results were obtained from the model with 1-dimensional Orbifold as an extra dimemsion.Masahiro Imachi, together with Hiroshi Yoneyama studied the numerical simulation to the theta terms in CP(2) models. The issue is the theta terms is imaginary in the path integration and hard to simulate in the ordinary algorisms. The Maximum Entropy Method (MEM) is a one major tool for this purpose. They found that even under MEM the flattening of the theta data cannot be avoided, the data that the flattening is resoled was just within a statistical error bar.

在该项目中，调查员塔罗·喀什瓦（Taro Kashiwa）研究了0和1维玻色子和费米子模型的辅助场方法（AFM）的有效性。在0-数字的情况下，发现在耦合常数的巨大范围内，1循环结果与确切的值非常吻合，并且出现的苛性剂，其特征是消失的第二个衍生物在该动作中消失了。在0-Dimensiona四fermi模型中的路径积分下的指数。具有双井潜力的一维玻璃体病例（量子生物案例）需要更高的循环校正，在该区域中，Instantons发挥了重要作用，可以通过引入其他辅助文件来纠正。现在正在研究。他们发现这个问题是，必须在一般坐标转换下转换布奇宾德 - 莱克霍维奇（BL）规范形式主义，通过BL与Ostrogradski形式主义的结合来解决。在这些模型的超对称扩展的情况下，可以解释生成的起源和组成粒子质量的总和规则。结果是从具有一维球形的模型获得的，作为额外的二聚体。MasahiroiMachi，以及Hiroshi Yoneyama一起研究了CP（2）模型中Theta项的数值模拟。问题是theta术语在路径整合中是虚构的，很难在普通算法中模拟。最大熵方法（MEM）是为此目的的一个主要工具。他们发现，即使在MEM下，也无法避免theta数据的变平，而扁平化的数据也仅在统计误差栏内。

项目成果

Effect of Dynamical SU(2) Gluons to the Gap Equation of Nambu--Jona-Lasinio Model in Constant Nonabelian Background Magnetic Field

恒定非阿贝尔背景磁场中动力SU(2)胶子对Nambu--Jona-Lasinio模型能隙方程的影响

• 发表时间: 2002
• 期刊: Physical Review D65
• 作者: Masaru Ishi-i;Taro Kashiwa;Naoki Tanimura
• 通讯作者: Naoki Tanimura

A canonical formalism of f(R)-type gravity in terms of Lie derivatives

用李导数表示的 f(R) 型引力的规范形式

• 发表时间: 2006
• 期刊: Classical and Quantum Gravity 23
• 作者: Y. Ezawa;H. Iwasaki;Y. Ohkuwa;T. Watanabe;N. Yamada;T. Yano
• 通讯作者: T. Yano

Dvnamical Theory of Generalized Matrices

广义矩阵动力学理论

• 发表时间: 2005
• 期刊: Progress of Theoretical Physics 114・3
• 作者: S. Sasaki;K. Orginos;S. Ohta;浦上 忠(分担執筆);Y.Kawamura
• 通讯作者: Y.Kawamura

例題・演習形式で学ぶ現代素粒子物理学

通过示例和练习学习现代粒子物理学

• 发表时间: 2006
• 作者: S. Aoki;et al.;川村嘉春
• 通讯作者: 川村嘉春

N.Haba, M.Harada.Y.Hosotani, Y.Kawamura: "Dynamical rearrangement of gauge symmetry on the orbifold"Nuclear Physics. B657. 169-213 (2003)

N.Haba、M.Harada.Y.Hosotani、Y.Kawamura：“轨道折叠上规范对称性的动态重排”核物理。