Budget Amount *help 
¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 2001 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 2000 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Research Abstract 
This research project was planned for advancement of understanding of the nonperturbative effects in quantum theory and further explore new possibilities of supersymmetry. The analytical method that can handle nonperturbative effects was the valley method in imaginary pathintegral formalism, developed a group including the current project leader, H. Aoyama. Using this method for an asymmetric doublewell potential model in onedimensional quantum mechanics, the Nfold supersymmetry had been found. Therefore it was intended to further explore this new supersymmetry, searching for new models. This fouryear research project has just accomplished this task. The valley method was applied to various quantum mechanical models. From the nonperturbative effects obtained by this method, the large order behaviour of perturbative series were extracted. Some of them lead to success : a periodic model was found to have a form of Nfold supersymmetry, which were more general than the assymmetric doublewell model, in a sense that its supercharge is not just the Nth power of the momentum, but an Nth order polynomial. Inspired by this finding, another model, a sextet model, was soon found to have an Nfold supersymmetry. All these Nfold supersymmetry models shared a special factorizable form of the supercharge. Motivated by this, we defined a subclass "typeA" of Nfold supersymmetry, and identified the necessary and sufficient conditions for Nfold supersymmetry. We solved these conditions completely, classified all the models of this type, and wrote down their potentials and supercharge. With these results, we now have a complete theory of typeA. Exploring models outside this subclass is one of the most important task for future.
