Non-perturbative Analysis of Field Theories by Renormalization Group

保持理论的非微扰动力学一直是粒子物理学中最重要的研究课题之一。然而，我们不能不说，目前的非微扰分析方法仍然处于相当差的水平。我们试图发展非微扰（精确）重整化群（RG）作为这样一种通用方法。我们研究了RG方程的形式和有效的逼近格式。我们还首次将非微扰反渗透方法应用于动力学手征对称性破缺这一粒子物理中非常重要的现象，并发展了分析方案。通过研究量子力学模型，用非微扰RG方法分析了瞬子效应等非微扰现象。作为副产品，我们发现RG方法能够捕获著名的自发超对称破缺。另一方面，我们研究了超对称规范理论中的非微扰动力学。特别是阐明了N=2超对称QCD真空的几个物理性质：对称性破缺、CP对称性、θ角依赖性、双子电荷等。

Non-perturbative dynamics of held theories has been one of the most important subject in particle physics. However we cannot help but saying that the present non-perturbative analytic methods are still in a rather poor level. We tried to develop the non-perturbative (exact) renormalization group (RG) as such a general method. We studied the formulation of the RG equations and the effective scheme of approximnation. Also we first have applied the non-perturbative RO to dynamical chiral symmetry breaking, which is quite significant phenomena in particle physics to be clarified, and developed the scheme of analysis. The non-perturbative phenomena like instanton effects have also analyzed through the non-perturbative RG method by studying the quantum mechanical models. As by-products, it has been found that the RG method is able to capture the famous spontaneous supersymmetry breaking.On the other hand we studied the non-perturbative dynamics in supersymmetric gauge thories. Especially we have clarified the several physical properties of N=2 supersymmetric QCD vacua ; symmetry breaking, CP symmetry, theta angle dependence, charges of dyons and so on.