3n-j Symbols
The 6-j symbol is the first representative, n=2, of 3n-j symbols that are defined as sums of products of n of Wigner's 3-jm coefficients. The sums are over all combinations of m that the 3n j-coefficients admit, i.e., which lead to non-vanishing contributions.
If each 3-jm factor is represented by a vertex and each j by an edge, these 3n-j symbols can be mapped on certain 3-regular graphs with 3n vertices and 2n nodes. The 6-j symbol is associated with the K4 graph on 4 vertices, the 9-j symbol with the utility graph on 6 vertices, and the two different (non-isomorphic) 12-j symbols with the Q_3 and Wagner graphs on 8 vertices. Symmetry relations are generally representative of the automorphism group of these graphs.
Read more about this topic: 9-j Symbol
Famous quotes containing the word symbols:
“Many older wealthy families have learned to instill a sense of public service in their offspring. But newly affluent middle-class parents have not acquired this skill. We are using our children as symbols of leisure-class standing without building in safeguards against an overweening sense of entitlement—a sense of entitlement that may incline some young people more toward the good life than toward the hard work that, for most of us, makes the good life possible.”
—David Elkind (20th century)