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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, : The summation is over all six allowed by the selection rules of the 3-j symbols. They are closely related to the Racah W-coefficients, which are used for recoupling 3 angular momenta, although Wigner 6-j symbols have higher symmetry and therefore provide a more efficient means of storing the recoupling coefficients. Their relationship is given by: : ==Symmetry relations== The 6-''j'' symbol is invariant under any permutation of the columns: : The 6-''j'' symbol is also invariant if upper and lower arguments are interchanged in any two columns: : These equations reflect the 24 symmetry operations of the automorphism group that leave the associated tetrahedral Yutsis graph with 6 edges invariant: mirror operations that exchange two vertices and a swap an adjacent pair of edges. The 6-''j'' symbol : is zero unless ''j''1, ''j''2, and ''j''3 satisfy triangle conditions, i.e., : In combination with the symmetry relation for interchanging upper and lower arguments this shows that triangle conditions must also be satisfied for the triads (''j''1, ''j''5, ''j''6), (''j''4, ''j''2, ''j''6), and (''j''4, ''j''5, ''j''3). Furthermore, the sum of each of the elements of a triad must be an integer. Therefore, the members of each triad are either all integers or contain one integer and two half-integers. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「6-j symbol」の詳細全文を読む スポンサード リンク
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