Wide applications of the renormalization group

我们将重整化群(RG)技术应用于量子场论和统计物理。Sonoda领导了量子场论的研究，西野领导了统计物理学的研究。在量子场论的应用中，得到了以下结果：1.通过考察大动量截断时RG方程的解的行为，引入了精确RG方程的解的参数化。将精确的RG方程转化为积分方程，给出了形式的摄动解。文1所述的参数化方法已应用于QED中。在统计物理中的应用中，得到了以下结果：1.发展了一种快速计算乘积波函数RG的数值方法。将矩阵乘积推广到张量积，建立了张量积RG变分方法，可以认为是密度矩阵RG方法在高维系统中的推广。对密度矩阵RG方法进行了推广，得到了随机光锥密度矩阵RG和快照生成方法。这些已应用于统计系统，产生了2维和3维ANNNI模型的相图，以及对称的16顶点模型。

We have applied renormalization group (RG) techniques to both quantum field theory and statistical physics. The research in quantum field theory was led by Sonoda, and that in statistical physics by Nishino.In the applications to quantum field theory, the following results have been obtained:1. Parametrization of the solutions to the exact RG equations was introduced by examining the behavior of the solutions at a large momentum cutoff2. The exact RG equation has been reformulated as an integral equation, which gives a formal perturbative solution.3. The parametrization described in 1 has been applied to QED. The Ward identities constrain the parameters.In the applications to statistical physics, the following results have been obtained:1. Avery fast numerical method of the product wave function RG has been developed.2. Generalizing the matrix products to tensor products, we have formulated the tensor product RG variational method, which can be considered as an extension of the density matrix RG method to higher dimensional systems.3. Extending the density matrix RG method, we have obtained the stochastic light-cone density matrix RG and the method of snapshot generation. These have been applied to statistical systems, resulting in phase diagrams of 2-and 3-dimensional ANNNI models, and the symmetric 16-vertex model.