"Quantum dilogarithm"의 두 판 사이의 차이
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| − | + | <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> |
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| − | < | + | <math>\sum_{n=0}^{\infty}\frac{q^{\frac{A}{2}n^2+cn}}{(q)_n}\sim\exp(\frac{C}{t})</math> |
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| − | + | 여기서 C는 [http://pythagoras0.springnote.com/pages/4855791 로저스 다이로그 함수 (Roger's dilogarithm)] 의 어떤 값에서의 합 | |
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| − | + | <h5 style="margin: 0px; line-height: 2em;">Knot and invariants from quantum dilogarithm</h5> | |
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| − | [ | + | * '''[Kashaev1995] '''<br> |
| + | * a link invariant, depending on a positive integer parameter N, has been defined via three-dimensional interpretation of the cyclic quantum dilogarithm<br> | ||
| + | * The construction can be considered as an example of the simplicial (combinatorial) version of the three-dimensional TQFT<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> | ||
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| − | <h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;"> | + | <h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">related items</h5> |
| − | + | * [[1 Fermion summation formula - quasi-particle interpretation|Boson and Fermion summation form]]<br> | |
| − | + | * [[asymptotic analysis of basic hypergeometric series]]<br> | |
| − | + | * [[quantum groups|Quantum groups]]<br> | |
| − | + | * [[Kashaev's volume conjecture|Kashaev's volume Conjecture]]<br> | |
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2011년 6월 30일 (목) 05:52 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.