2006 Fiscal Year Final Research Report Summary
Quantum Field Theory on Noncommutative Space and Its Applications
| Project/Area Number |
13135202
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Tohoku University |
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Principal Investigator |
EZAWA Zyun F. Tohoku University, Graduate School of Science, Professor (90133925)
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| Co-Investigator(Kenkyū-buntansha) |
WATAMURA Satoshi TOHOKU UNIVERSITY, Graduate School of Science, Associate Professor (00201252)
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| Project Period (FY) |
2001 – 2006
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| Keywords | Noncommutative Space / Noncommutatie Soliton / Instanton / Quantum Hall Effects / String Theory / Noncommutative Superspace / Nahm Duality / ADHM Construction |
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| Research Abstract |
Z. F. Ezawa made an investigation on quantum Hall (QH) systems as an application of the quantum field theory on noncommutative space. The QH system is a world of planar electrons, where the x and y coordinates become noncommutative. When the electron possesses the SU(N)symmetry,the algebraic structure becomes the SU(N)extension of the W_∞ algebra,which he has named the W_∞(N)algebra. Due to the noncommutativity he has shown that quantum coherence develops spontaneously driven by the exchange interaction between electrons. This theoretical result is experimentally testable by observing topological solitons associated with the quantum coherence. It is intriguing that the topological soliton is a noncommutative soliton in QH systems. As one of the main results, he has constructed the quantum mechanical state of a noncommutative soliton (skyrmion) by making a W_∞(N)rotation of a hole state. Furthermore, calculating the excitation energy of a skyrmion both in the monolayer QH system and the
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bilayer QH system, he has compared successfully his theoretical results with the experimental data.
S. Watamura has studied non-trivial configurations in the gauge theory on the non-(anti)commutative spaces which are emerging from the superstring theory. This research is important to understand the properties of a D-brane. Especially, he has constructed a non-trivial configuration, the monopole bundle on the Fuzzy sphere by using the projective module construction. Generalizing that method, he could clarify the structure of the bundles on concommutative CPn. On the one hand, in 4-dimensional space one can solve this problem by using the so-called ADHM construction. He then generalized the ADHM method to the non-anticommutative superspace and analyzed the moduli space by constructing the instanton solutions. Applying the superfield method on this problem was an open problem even in the commutative case. He has succeeded to construct the Instanton solutions completely in the superspace, including the gauge fixing. He has shown the deformation of the fermionic and bosonic moduli space corresponding to the deformed instanton solution generalized to the nonanticommutative case. Less
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