"Quantum dilogarithm"의 두 판 사이의 차이
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<h5 style="margin: 0px; line-height: 2em;">근사 공식</h5> | <h5 style="margin: 0px; line-height: 2em;">근사 공식</h5> | ||
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* <math>q=e^{-t}</math> and as the t goes 0 (i.e. as q goes to 1)<br> | * <math>q=e^{-t}</math> and as the t goes 0 (i.e. as q goes to 1)<br> | ||
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* this invariant is in fact a quantum generalization of the hyperbolic volume invariant.<br> | * this invariant is in fact a quantum generalization of the hyperbolic volume invariant.<br> | ||
* It is possible that the simplicialTQFT, defined in terms of the cyclic quantum dilogarithm, can be associated with quantum 2 + 1-dimensional gravity.<br> | * It is possible that the simplicialTQFT, defined in terms of the cyclic quantum dilogarithm, can be associated with quantum 2 + 1-dimensional gravity.<br> | ||
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| + | * '''[Kashaev1995]'''[http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm]<br> | ||
| + | ** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418 | ||
2011년 8월 19일 (금) 00:35 판
introduction[1]
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