"Quantum dilogarithm"의 두 판 사이의 차이
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* Kashaev, http://arxiv.org/abs/1104.4630[[분류:개인노트]] | * Kashaev, http://arxiv.org/abs/1104.4630[[분류:개인노트]] | ||
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2012년 10월 29일 (월) 03:08 판
introduction
근사 공식
- \(q=e^{-t}\) and as the t goes 0 (i.e. as q goes to 1)
\(\sum_{n=0}^{\infty}\frac{q^{\frac{A}{2}n^2+cn}}{(q)_n}\sim\exp(\frac{C}{t})\)
여기서 C는 로저스 다이로그 함수 (Roger's dilogarithm) 의 어떤 값에서의 합
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
quantum dilogarithm identities
- Boson and Fermion summation form
- asymptotic analysis of basic hypergeometric series
- Quantum groups
- Kashaev's volume Conjecture
expositions
- Quiver mutations and quantum dilogarithm identities, presentation, Isle of Skye, June 27, 2011
- Quantum dilogarithm identities from quiver mutations, video of a talk given at Banff, September 9, 2010.
articles
- Keller, http://arxiv.org/abs/1102.4148
- Kashaev, http://arxiv.org/abs/1104.4630