Quantumgroup Theoretical Extension of Rotation Group・Symmetric Group and Its Application to Manybody Problems
Project/Area Number  07640525 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
物理学一般

Research Institution  The University of Tokyo 
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)

Project Fiscal Year 
1995 – 1997

Project Status 
Completed(Fiscal Year 1997)

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)

Keywords  quantum groups / covariant formalism / YangBaxter relations / rotation groups / symmetric groups / Racah algebra / Young diagrams / knot theory / 量子群 / 共変理論 / YangBaxter関係式 / 回転群 / 対称群 / ラカ代数 / ヤング図表 / くみひも理論 / 第二量子化法 
Research Abstract 
WignerRacah 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 qcovariant way according to coordinate transformation in qspace. This formalism suggests application to manybody theory in nuclear physics. New qdeformation is investigated also on symmetric group characters. Main results are summarized as follows : Systematic qextension of Boson/Fermion creationannihilation operators. New relationship is found between qextended 3nj symbol of the first kind (which the author exploited) and YangBaxter 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 qfunctions such as qClebschGordan (qCG) and qRacah coefficients. It leads to new systematic finding of novel identities on 3nj symbols. A new type of qdeformed symmetric group characters is found for Sn with n<less than or equal>5. This qextension, which is based on a physical model, is essentially different from usual qcharacters inherent to Hecke al Possibilities are found to use qCG 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.

Report
(5results)
Research Output
(4results)