9-j Symbol - 3n-j Symbols

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:

    Luckless is the country in which the symbols of procreation are the objects of shame, while the agents of destruction are honored! And yet you call that member your pudendum, or shameful part, as if there were anything more glorious than creating life, or anything more atrocious than taking it away.
    Savinien Cyrano De Bergerac (1619–1655)