"Quantum dilogarithm"의 두 판 사이의 차이
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introduction==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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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;">introduction | + | <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;">introduction== |
* [http://pythagoras0.springnote.com/pages/7978406 양자 다이로그 함수(quantum dilogarithm)] | * [http://pythagoras0.springnote.com/pages/7978406 양자 다이로그 함수(quantum dilogarithm)] | ||
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| − | <h5 style="margin: 0px; line-height: 2em;">근사 공식 | + | <h5 style="margin: 0px; line-height: 2em;">근사 공식== |
* <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> | ||
| 23번째 줄: | 23번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">Knot and invariants from quantum dilogarithm | + | <h5 style="margin: 0px; line-height: 2em;">Knot and invariants from quantum dilogarithm== |
* '''[Kashaev1995] '''<br> | * '''[Kashaev1995] '''<br> | ||
| 40번째 줄: | 40번째 줄: | ||
| − | ==quantum dilogarithm identities | + | ==quantum dilogarithm identities== |
| 50번째 줄: | 50번째 줄: | ||
| − | <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 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== |
* [[1 Fermion summation formula - quasi-particle interpretation|Boson and Fermion summation form]]<br> | * [[1 Fermion summation formula - quasi-particle interpretation|Boson and Fermion summation form]]<br> | ||
| 59번째 줄: | 59번째 줄: | ||
| − | ==expositions | + | ==expositions== |
* [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, 2011 | * [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, 2011 | ||
| 68번째 줄: | 68번째 줄: | ||
| − | <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 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== |
* Keller, http://arxiv.org/abs/1102.4148 | * Keller, http://arxiv.org/abs/1102.4148 | ||
* Kashaev, http://arxiv.org/abs/1104.4630 | * Kashaev, http://arxiv.org/abs/1104.4630 | ||
2012년 10월 28일 (일) 14:37 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
- \(q=e^{-t}\) and as the t goes 0 (i.e. as q goes to 1)
- [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