| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
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| Research Abstract |
The purpose of this project has been to study the physical significance of topological structures of quantum field theory, and find its possible applications in physics. To this end, I have investigated a typical field theory model of elementary particle physics which possesses topological structures, and also studied one dimensional systems with singularity which can be regarded as a topological structure in the most fundamental sense. The results are as follows.
(1)Low energy effective QCD as a field theory model with topological structures
A viable model of the low energy QCD is, according to Faddeev and Niemi, the non-linear sigma model with a topological term. My analysis of the topological aspects of the model shows that the instanton configurations of the gluon gauge fields, arise as monopoles in the non-linear sigma model where tow topological charges are directly related. In the latter model, the monopoles are also related to the Hopi solitons, whose charge is argued to give a measure of the energy of the excitations which may be considered to be glue balls.
(2)One dimensional system with singularity and recurrence phenomena
Since topological aspects of quantum field theory are deeply related to the singularity of configurations, the study of singularity in quantum mechanics is crucial to understand the former. My investigation of systems with quantum point (singular) interactions on a line has uncovered the fact that they are parameterized by the group U(2), and that those phenomena which are normally ascribed to some topological structure of quantum theory, such as Berry phase and duality, can indeed be associated with the singularity of the system. Moreover, in analyzing another type of singularity which arises in divergent potentials, I found that a system may exhibit recurrence phenomena due to quantum tunneling and caustics, which can be used to build
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