Quantum dilogarithm

introduction

\(q=e^{-t}\) and as the t goes 0 (i.e. as q goes to 1) \[\sum_{n=0}^{\infty}\frac{q^{\frac{A}{2}n^2+cn}}{(q)_n}\sim\exp(\frac{C}{t})\]

[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