Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem

Details Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem

2010-09-12

arxiv.org/abs/1009.2261v2

Mathematics

Quantum Algebra

11 pages, iopart, BibTeX

Scientific paper

A well known recurrence relation for the 6j-symbol of the quantum group su_q(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking advantage of existing specialized numerical packages. For convenience, all formulas relevant for such an implementation are collected in the appendix. This realization is a byproduct of an alternative proof of the recurrence relation, which generalizes a classical (q=1) result of Schulten and Gordon and uses the diagrammatic spin network formalism of Temperley-Lieb recoupling theory to simplify intermediate calculations.

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