"Quantum dilogarithm"의 두 판 사이의 차이
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imported>Pythagoras0 |
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* {{수학노트|url=양자_다이로그_함수(quantum_dilogarithm)}} | * {{수학노트|url=양자_다이로그_함수(quantum_dilogarithm)}} | ||
| − | * http://arxiv.org/abs/hep-th/ | + | * {{수학노트|url=양자_다이로그_항등식_(quantum_dilogarithm_identities)}} |
| + | * http://arxiv.org/abs/hep-th/9611117 | ||
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==근사 공식== | ==근사 공식== | ||
| − | * <math>q=e^{-t}</math> | + | * <math>q=e^{-t}</math> and as the t goes 0 (i.e. as q goes to 1) :<math>\sum_{n=0}^{\infty}\frac{q^{\frac{A}{2}n^2+cn}}{(q)_n}\sim\exp(\frac{C}{t})</math> |
여기서 C는 [http://pythagoras0.springnote.com/pages/4855791 로저스 다이로그 함수 (Roger's dilogarithm)] 의 어떤 값에서의 합 | 여기서 C는 [http://pythagoras0.springnote.com/pages/4855791 로저스 다이로그 함수 (Roger's dilogarithm)] 의 어떤 값에서의 합 | ||
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| − | ==Knot | + | ==Knot and invariants from quantum dilogarithm== |
| − | * '''[Kashaev1995] | + | * '''[Kashaev1995] ''' |
| − | * a link invariant, depending on a positive integer parameter N, | + | * 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 | + | * 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. | + | * 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 | + | * It is possible that the simplicialTQFT, defined in terms of the cyclic quantum dilogarithm, can be associated with quantum 2 + 1-dimensional gravity. |
| − | * '''[Kashaev1995]'''[http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm] | + | * '''[Kashaev1995]'''[http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm] |
| − | ** Kashaev, R. M., | + | ** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418 |
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==related items== | ==related items== | ||
| − | * [[Fermionic summation formula]] | + | * [[Fermionic summation formula]] |
| − | * [[asymptotic analysis of basic hypergeometric series]] | + | * [[asymptotic analysis of basic hypergeometric series]] |
| − | + | * [[Kashaev's volume conjecture|Kashaev's volume Conjecture]] | |
| − | * [[Kashaev's volume conjecture|Kashaev's volume Conjecture]] | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
2013년 5월 30일 (목) 02:50 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