Non-perturbative Analysis of Field Theories by Renormalization Group

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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.