| Project/Area Number |
07640525
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | The University of Tokyo |
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Principal Investigator |
NOMURA Masao The University of Tokyo, Graduate School of Arts and Science, Professor, 大学院・総合文化研究所, 教授 (10012402)
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| Project Period (FY) |
1995 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1997: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1996: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1995: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | quantum groups / covariant formalism / Yang-Baxter relations / rotation groups / symmetric groups / Racah algebra / Young diagrams / knot theory / 第二量子化法 |
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| Research Abstract |
Wigner-Racah algebras on angular momentum are extended to quantum (q-) group algebras so that the tensors (physical quantities) as well as the generators should be transformed in q-covariant way according to coordinate transformation in q-space. This formalism suggests application to many-body theory in nuclear physics. New q-deformation is investigated also on symmetric group characters. Main results are summarized as follows :
Systematic q-extension of Boson/Fermion creation-annihilation operators.
New relationship is found between q-extended 3nj symbol of the first kind (which the author exploited) and Yang-Baxter relation of the face model.
Remarkably simply expressions are obtained for the first and the second differential coefficients by q at q*1 of various q-functions such as q-Clebsch-Gordan (q-CG) and q-Racah coefficients. It leads to new systematic finding of novel identities on 3nj symbols.
A new type of q-deformed symmetric group characters is found for Sn with n<less than or equal>5. This q-extension, which is based on a physical model, is essentially different from usual q-characters inherent to Hecke al
Possibilities are found to use q-CG coefficients, which satisfy the same types of orthogonalities as those of SU (2), as transformation coefficients in helicity representation, pseudo LS coupling, etc.of the usual formalism.
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