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Systems with Spontaneously Broken Symmetries and Nonperturbative Methods

对称性自发破缺的系统和非微扰方法

基本信息

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

项目摘要

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.

在这个项目中，首席研究员Taro Kashiwa研究了辅助场方法（AFM）在0和1维玻色子和费米子模型中的有效性。在0维情况下，发现在耦合常数的大范围内，1环结果与精确值拟合得很好，并且在0维四费米模型中出现焦散，其特征是路径积分下指数作用的二阶导数消失。具有双阱势的一维波什尼奇情况（量子力学情况）在瞬子起重要作用的区域需要更高的环路修正，这可以通过引入额外的辅助场来治愈。此事目前正在调查中。江泽康夫研究了包含高导数的引力理论；他们发现了Buchbinder-Lyakhovich （BL）规范形式主义中的哈密顿量必须在一般坐标变换下进行变换的问题，通过BL与Ostrogradski形式主义的结合解决了这一问题。Yoshiharu Kawamura发现了五维时空中的大统一模型，可以解释这些模型的超对称扩展情况下组成粒子质量的起源和和规则。结果是在以一维轨道作为额外维度的模型中得到的。Masahiro Imachi和Hiroshi Yoneyama一起研究了CP(2)模型中theta项的数值模拟。问题是在路径积分中θ项是虚的在普通算法中很难模拟。最大熵法（MEM）是实现这一目的的一个主要工具。他们发现，即使在MEM下，theta数据的平坦化也无法避免，平坦化被解决的数据只是在统计误差条内。