Recoupling theory for quantum spinors

TL;DR

This paper develops a recoupling theory for quantum spinors by extending the Birman-Wenzl category to include spin representations, resulting in a q-analogue of chromatic evaluation and Fierz coefficients.

Contribution

It introduces a novel extension of the Birman-Wenzl category incorporating spin representations and develops the associated recoupling theory with q-analogues.

Findings

Extended Birman-Wenzl category with spin representations

Developed q-analogue of chromatic evaluation for spin networks

Evaluated q-analogues of Fierz coefficients

Abstract

This paper extends the Birman-Wenzl category by including a spin representation and then developing the recoupling theory, following Cvitanovic. In particular this gives a q-analogue of the chromatic evaluation of a spin network. The recoupling theory is developed up to an evaluation of the q-analogues of the Fierz coefficients.