Skein relations for spin networks, modified
Abstract
An alternative framework underlying connection between tensor ${\rm sl}_2$calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for the diagrammatic recoupling methods. Yet it preserves the standard chromatic graph evaluations. In contrast with the standard formulation, the background space is that of symmetric tensor spaces, which seems to be in accordance with the representation theory of ${\rm SL}(2)$. An example of Apollonian disk packing is shown to be a source of spin networks. The graph labeling is extended to noninteger values, resulting in the complexvalues of chromatic evaluations.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 DOI:
 10.48550/arXiv.1807.07244
 arXiv:
 arXiv:1807.07244
 Bibcode:
 2018arXiv180707244K
 Keywords:

 Mathematical Physics;
 20C35;
 57M25;
 57M27
 EPrint:
 21 pages, lots of diagrams. Preprint of an article accepted for publication in Journal of Knot Theory and Its Ramifications [2018], World Scientific Publishing Company