SU（2）群的第一类和第二类$3n-j (j > 2)$符号的泛因式分解及其直接精确计算和制表
Universal Factorization of $3n-j (j > 2)$ Symbols of the First and Second Kinds for SU(2) Group and Their Direct and Exact Calculation and Tabulation
摘要：
我们证明了SU（2）群的第一类和第二类一般$3n-j (n>2)$符号可以用二项式系数重新表示。证明是基于由Yutsis等人建立的图形技术，并通过一个减少的$6-j$符号的定义。由此得到的$3n-j$符号采用简单地为两个因子的乘积的组合形式。一个是整数或多项式，它是简化的$6-j$符号的乘积的单个和。它们的形式是对二项式系数的乘积求和。另一个是符号中出现的所有三角关系的乘法，也可以使用二项式系数重写。新的公式表明广义再耦合系数的内在结构更好、更简单，可以作为与其他领域研究的桥梁。随着我们新开发的算法，这也提供了一个基础，直接，准确和有效的计算或列表的所有$3n-j$符号的SU（2）群的所有范围内的量子角动量的论点。作为一个例子，我们给出了第一类$12-j$符号的结果.
英文摘要：
We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and through a definition of a reduced $6-j$ symbol. The resulting $3n-j$ symbols thereby take a combinatorial form which is simply the product of two factors. The one is an integer or polynomial which is the single sum over the products of reduced $6-j$ symbols. They are in the form of summing over the products of binomial coefficients. The other is a multiplication of all the triangle relations appearing in the symbols, which can also be rewritten using binomial coefficients. The new formulation indicates that the intrinsic structure for the general recoupling coefficients is much nicer and simpler, which might serves as a bridge for the study with other fields. Along with our newly developed algorithms, this also provides a basis for a direct, exact and efficient calculation or tabulation of all the $3n-j$ symbols of the SU(2) group for all range of quantum angular momentum arguments. As an illustration, we present teh results for the $12-j$ symbols of the first kind.
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