Systems with Spontaneously Broken Symmetries and Nonperturbative Methods

在这个项目中，首席研究员鹿河太郎研究了辅助场方法(AFM)在0维和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圈的结果与精确值很好地吻合，并且在0维四费米模型中出现焦散，其特征是在路径积分下作用在指数中的二阶导数消失。具有双势垒势的一维玻色情形(量子机械论情形)需要在瞬子起重要作用的区域进行更高的回路修正，这将通过引入额外的辅助场来解决。这一点目前正在研究中。江泽康夫研究了包含高阶导数的引力理论；他们发现，Buchbinder-Lyakhovich(BL)正则形式中的哈密顿量必须在一般坐标变换下变换，通过BL与Ostrogradski形式的结合来解决。川村佳治在5维时空中发现了大统一模型，该模型可以解释组成粒子质量的产生的起源和在这些模型超对称扩展的情况下的求和规则。结果是从一维Orbilold模型中得到的，Masahiro Imachi和Hiroshi Yoneyama研究了CP(2)模型中的theta项的数值模拟。问题是，theta项在路径积分中是虚构的，在普通算法中很难模拟。最大熵方法(MEM)是实现这一目的的主要工具之一。他们发现，即使在MEM下，theta数据的扁平化也无法避免，扁平化得到解决的数据只是在统计误差栏内。

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.