Wigner's 6-j symbols were introduced by Eugene Paul Wigner in 1940 and published in 1965. They are defined as a sum over products of four Wigner 3-j symbols,

This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. As an imaginary unit, use i or j (in electrical engineering), which satisfies the basic equation i 2 = −1 or j 2 = −1. The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar ...

由6j-符号和3j-符号的关系的结构可以看出，6j-符号必须满足四种角动量 耦合关系，否则6j-符号便为0，通过使用 速记符号，用电来表示角动量，可以得到耦合方式如下图所示。 同时也给出集中经常用到的对称性质。 1. \begin {align} \left\ { \begin {array} {ccc} j_1&j_2&j_3 \\ l_1&l_2&l_3 \end {array} \right\}=0 \end {align} 当上图中的四种耦合方式无法全部满足时，即 (j_1j_2j_3) 、 (j_1l_2l_3) 、 (l_1l_2j_3) 、 (l_1j_2l_3) ，6j-系数为0。

2025年3月5日 · The Wigner 6j-symbols (Messiah 1962, p. 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in the coupling of three angular momenta. They are variously called the "6j symbols" (Messiah 1962, p. 1062) or 6-j symbols (Shore and Menzel 1968, p. 279).

SixJSymbol [ {j1, j2, j3}, {j4, j5, j6}] 给出 Wigner 6-j 符号的值.

\begin{equation} \begin{aligned} & \left\{\begin{matrix}j_1 & j_2 & j_3\\ j_4 & j_5 & j_6\end{matrix}\right\} = \sum_{m_1, \dots, m_6} (-1)^{\sum_{k= 1}^6 (j_k - m_k)} \begin{pmatrix}j_1 & j_2 & j_3\\ -m_1 & -m_2 & -m_3\end{pmatrix} \times\\ & \begin{pmatrix}j_1 & j_5 & j_6\\ m_1 & -m_5 & m_6\end{pmatrix} \begin{pmatrix}j_4 & j_2 & j_6\\ m_4 ...

We identify the 6j-symbols of generic representations of $U_\epsilon sl2\mathbb{C}$, the main ingredients of QHFT, with a bundle morphism defined over a finite cover of the algebraic quotient $PSL...

SixJSymbol [ {j1, j2, j3}, {j4, j5, j6}] gives the values of the Wigner 6-j symbol.

2019年4月10日 · We study 6j-symbols or Racah coefficients for the tensor products of infinite-dimensional unitary principal series representations of the group SL(2, ℂ). Using the Feynman diagram technique, we reproduce the results of Ismagilov in constructing these symbols (up to a slight difference associated with equivalent representations).

EXPLICIT FORMS OF THE 6j SYMBOLS FOR CERTAIN ARGUMENTS . One of Arguments is Equal to Zero. One of Arguments is Equal to the Sum of Two Others. One of Arguments is Smaller by Unity than the Sum of Two Others. Arguments a, b, d, e are Equal in Pairs. RECURSION RELATIONS . Relations in Which Arguments are Changed by 1/2. Relations in …