nLab 10j symbol

In the context of fixed triangulations of spacetime arising in spin foam models?, the 10j symbol is a spin network that arises in the partition function for the Barrett-Crane model? of Riemannian quantum gravity?. Greg Egan, J. Daniel Christensen, and John Baez formulated an algorithm in C++ to describe these symbols that arise in this discrete spin foam model.

Definition

A 10j symbol is a spin(4) spin network containing five vertices and ten edges, where the edges are labels by spins. This symbol can be understood as a function which receives ten spins as input and produces a complex number as output, this process underpins the calculation of the partition function for the Barrett-Crane model?, which depends on the contraction of tensors at the vertices.

References

• J. Daniel Christensen and Greg Egan, An Efficient Algorithm for the Riemannian 10j Symbols. arxiv:gr-qc/0110045v3

• John C. Baez, J. Daniel Christensen, and Greg Egan. Asymptotics of 10j Symbols Classical and Quantum Gravity 19, no. 24 (December 21, 2002): 6489–6513. arXiv:gr-qc/0208010