| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1993: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1992: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1991: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Research Abstract |
In the past three years, we have studied (1) a possibility of a dynamical generation of a local gauge symmetry in quantum field theory, and (2) some problems in the quantum cosmology.
1. Usually one belives that the gauge symmetry in our world is being imposed as a principle form the out set, and then it is destroyed in low energy region by the spontaneous symmetry breakdown. Hence the higher symmetry is observed as the energy increased. In our research, however, we found an opposite case, i. e., the symmetry in low energy is higher than the one originally imposed. This phenomenon occurs when a part of the space-time is compactified by the Kakuza-Klein mechanism(KKM). Although KKM reduces the original symmetry, a new mechanism generates a new dynamical gauge symmetry. This is able to be identified with a berry phase effect. The model demonstrated here is a U(1) gauge theory in the 6-d Minkowski space M_4. If M_6 is compacitified into M_4 times a 2-d compact Riemann surface with genus g, T_8, the gouge symmetry in the space M_4 becames [U(1)]^g. The kinetic ebergy terms for the gauge fields are proven to ve generated. The fields can be associated terms for the gauge fields are proven to be generated. The fields can be associated with the solenoid fields of T_g.
The mechanism can be extended for the generation of non-abelian theory.
2. In quantum cosmology we studied the dual string theories in critical dimensions as a model of two dimennsional quantum cosmology. We identified all observables that intelligent creatures who live in the 2-d universe could observe. They can recognize the target space structure. The study suggests us a many of new interpretations of physical concepts. The spin and the isospin, for instance, are able to ve interpreted on the asme footing.
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