"Quantum dilogarithm"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| 19번째 줄: | 19번째 줄: | ||
==Teschner's version== | ==Teschner's version== | ||
| − | * | + | * <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> |
2020년 11월 16일 (월) 05:26 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