"Quantum dilogarithm"의 두 판 사이의 차이
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| − | * [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, | + | * [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, 2011 |
* [http://www.birs.ca/events/2010/5-day-workshops/10w5069/videos Quantum dilogarithm identities from quiver mutations], video of a talk given at Banff, September 9, 2010. | * [http://www.birs.ca/events/2010/5-day-workshops/10w5069/videos Quantum dilogarithm identities from quiver mutations], video of a talk given at Banff, September 9, 2010. | ||
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| + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | ||
* Keller, http://arxiv.org/abs/1102.4148 | * Keller, http://arxiv.org/abs/1102.4148 | ||
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* Kashaev, http://arxiv.org/abs/1104.4630 | * Kashaev, http://arxiv.org/abs/1104.4630 | ||
2012년 8월 26일 (일) 13:43 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