Quantum dilogarithm

introduction

[Kashaev1995]
a link invariant, depending on a positive integer parameter N, has been defined via three-dimensional interpretation of the cyclic quantum dilogarithm
The construction can be considered as an example of the simplicial (combinatorial) version of the three-dimensional TQFT
this invariant is in fact a quantum generalization of the hyperbolic volume invariant.
It is possible that the simplicialTQFT, defined in terms of the cyclic quantum dilogarithm, can be associated with quantum 2 + 1-dimensional gravity.

[Kashaev1995]A link invariant from quantum dilogarithm
- Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418

<math>b\in \R_{>0}</math>
<math>G_b(z)</math>
<math>G_b(z+Q)=G_b(z)(1-e^{2\pi ib z})(1-e^{2\pi ib^{-1}z})</math>, where <math>Q=b+b^{-1}</math>