Quantum-group Theoretical Extension of Rotation Group・Symmetric Group and Its Application to Many-body Problems

旋转群·对称群的量子群理论推广及其在多体问题中的应用

• 批准号: 07640525
• 负责人: NOMURA Masao
• 金额: $ 1.47万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640525/
• 关键词: quantum groups; covariant formalism; Yang-Baxter relations; rotation groups; symmetric groups; Racah algebra; Young diagrams; knot theory; 第二量子化法

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 alPossibilities 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.

将角动量上的Wigner-Racah代数推广到量子（q-）群代数中，使张量（物理量）和生成子根据q空间中的坐标变换进行q协变变换。这种形式主义建议应用于核物理中的多体理论。在对称群特征上研究了新的q-变形。主要研究结果如下：玻色子/费米子产生湮灭算子的系统q扩展。在第一类q-扩展3nj符号（作者利用的）与人脸模型的Yang-Baxter关系之间发现了新的关系。对于各种q函数，如q- clebsch - gordan （q- cg）和q- racah系数，通过q在q*1处得到了一阶和二阶微分系数的非常简单的表达式。这导致了对3nj符号新身份的系统发现。对于n<小于等于bbb5的Sn，发现了一类新的q变形对称群字符。这种基于物理模型的q-扩展与Hecke固有的q-字符有本质上的不同。我们发现了使用q-CG系数作为通常形式化的螺旋表示、伪LS耦合等变换系数的可能性，这些系数满足与SU(2)相同的正交性类型。

项目成果

M.Nomura: "Racah coefficieuts in g-couariant formalisn" Proceeding of lnternational Hutsulian Workshop (Rakhiv,1995). (1998)

M.Nomura：“g-couariant 形式化中的 Racah coefficieuts”国际 Hutsulian 研讨会论文集（Rakhiv，1995）。

野村 正雄: "Covauiant g-Algebras -As Extended Wiger Racah Algebras-" (交渉中), 500 (1998)

Masao Nomura：“Covauiant g-Algebras -As Extended Wiger Racah Algebras-”（正在协商中），500 (1998)