Quantum dilogarithm
imported>Pythagoras0님의 2020년 11월 12일 (목) 23:28 판
introduction
Knot and invariants from quantum dilogarithm
- [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
Teschner's version
- $b\in \R_{>0}$
- $G_b(z)$
- $G_b(z+Q)=G_b(z)(1-e^{2\pi ib z})(1-e^{2\pi ib^{-1}z})$, where $Q=b+b^{-1}$
- Manufacturing matrices from lower ranks
- Fermionic summation formula
- asymptotic analysis of basic hypergeometric series
- Kashaev's volume conjecture