"Quantum dilogarithm"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 3명의 중간 판 51개는 보이지 않습니다) | |||
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| − | + | ==introduction== | |
| − | + | * {{수학노트|url=양자_다이로그_함수(quantum_dilogarithm)}} | |
| + | * {{수학노트|url=양자_다이로그_항등식_(quantum_dilogarithm_identities)}} | ||
| + | * http://arxiv.org/abs/hep-th/9611117 | ||
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| − | + | ==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]'''[http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm] | |
| + | ** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418 | ||
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| − | http:// | + | ==Teschner's version== |
| + | * <math>b\in \R_{>0}</math> | ||
| + | * <math>G_b(z)</math> | ||
| + | * <math>G_b(z+Q)=G_b(z)(1-e^{2\pi ib z})(1-e^{2\pi ib^{-1}z})</math>, where <math>Q=b+b^{-1}</math> | ||
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| + | ==related items== | ||
| + | * [[Manufacturing matrices from lower ranks]] | ||
| + | * [[Fermionic summation formula]] | ||
| + | * [[asymptotic analysis of basic hypergeometric series]] | ||
| + | * [[Kashaev's volume conjecture]] | ||
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| + | ==computational resource== | ||
| + | * https://drive.google.com/file/d/0B8XXo8Tve1cxQ09YeHM2ellGS1U/view | ||
| + | * http://math-www.uni-paderborn.de/~axel/graphs/ | ||
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| + | [[분류:개인노트]] | ||
| + | [[분류:Number theory and physics]] | ||
| + | [[분류:dilogarithm]] | ||
| + | [[분류:migrate]] | ||
| + | |||
| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q7269036 Q7269036] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'quantum'}, {'LEMMA': 'dilogarithm'}] | ||
2021년 2월 17일 (수) 02:08 기준 최신판
introduction
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
Teschner's version
- \(b\in \R_{>0}\)
- \(G_b(z)\)
- \(G_b(z+Q)=G_b(z)(1-e^{2\pi ib z})(1-e^{2\pi ib^{-1}z})\), where \(Q=b+b^{-1}\)
- Manufacturing matrices from lower ranks
- Fermionic summation formula
- asymptotic analysis of basic hypergeometric series
- Kashaev's volume conjecture
computational resource
- https://drive.google.com/file/d/0B8XXo8Tve1cxQ09YeHM2ellGS1U/view
- http://math-www.uni-paderborn.de/~axel/graphs/
메타데이터
위키데이터
- ID : Q7269036
Spacy 패턴 목록
- [{'LOWER': 'quantum'}, {'LEMMA': 'dilogarithm'}]