Universal factorization of 3nj(j > 2) symbols of the first and second kinds for SU(2) group and their direct and exact calculation and tabulation
Abstract
We show that general 3nj(n > 2) symbols of the first and second kinds 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 6j symbol. The resulting 3nj 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 6j 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 serve as a bridge for 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 3nj symbols of the SU(2) group for all the range of quantum angular momentum arguments. As an illustration, we present the results for the 12j symbols of the first kind.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2004
 DOI:
 10.1088/03054470/37/9/014
 arXiv:
 arXiv:mathph/0306040
 Bibcode:
 2004JPhA...37.3259W
 Keywords:

 Mathematical Physics
 EPrint:
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