"Quantum dilogarithm"의 두 판 사이의 차이

수학노트
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(사용자 2명의 중간 판 22개는 보이지 않습니다)
1번째 줄: 1번째 줄:
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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>
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==introduction==
  
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* [http://pythagoras0.springnote.com/pages/7978406 양자 다이로그 함수(quantum dilogarithm)]
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* {{수학노트|url=양자_다이로그_함수(quantum_dilogarithm)}}
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* {{수학노트|url=양자_다이로그_항등식_(quantum_dilogarithm_identities)}}
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* http://arxiv.org/abs/hep-th/9611117
  
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==Knot and invariants from quantum dilogarithm==
  
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<h5 style="margin: 0px; line-height: 2em;">근사 공식</h5>
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* '''[Kashaev1995] '''
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*  a link invariant, depending on a positive integer parameter N, has been defined via three-dimensional interpretation of the cyclic quantum dilogarithm
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*  The construction can be considered as an example of the simplicial (combinatorial) version of the three-dimensional TQFT
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*  this invariant is in fact a quantum generalization of the hyperbolic volume invariant.
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*  It is possible that the simplicialTQFT, defined in terms of the cyclic quantum dilogarithm, can be associated with quantum 2 + 1-dimensional gravity.
  
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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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* '''[Kashaev1995]'''[http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm]
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** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418
  
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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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==Teschner's version==
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* <math>b\in \R_{>0}</math>
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* <math>G_b(z)</math>
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* <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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여기서 C는 [http://pythagoras0.springnote.com/pages/4855791 로저스 다이로그 함수 (Roger's dilogarithm)] 의 어떤 값에서의 합
 
  
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==related items==
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* [[Manufacturing matrices from lower ranks]]
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* [[Fermionic summation formula]]
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* [[asymptotic analysis of basic hypergeometric series]]
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* [[Kashaev's volume conjecture]]
  
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==computational resource==
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* https://drive.google.com/file/d/0B8XXo8Tve1cxQ09YeHM2ellGS1U/view
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* http://math-www.uni-paderborn.de/~axel/graphs/
  
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<h5 style="margin: 0px; line-height: 2em;">Knot and invariants from quantum dilogarithm</h5>
 
  
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* '''[Kashaev1995] '''<br>
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[[분류:개인노트]]
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*  a link invariant, depending on a positive integer parameter N, has been defined via three-dimensional interpretation of the cyclic quantum dilogarithm<br>
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[[분류:Number theory and physics]]
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*  The construction can be considered as an example of the simplicial (combinatorial) version of the three-dimensional TQFT<br>
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[[분류:dilogarithm]]
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*  this invariant is in fact a quantum generalization of the hyperbolic volume invariant.<br>
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[[분류:migrate]]
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*  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>
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==메타데이터==
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** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q7269036 Q7269036]
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===Spacy 패턴 목록===
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* [{'LOWER': 'quantum'}, {'LEMMA': 'dilogarithm'}]
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<h5>quantum dilogarithm identities</h5>
 
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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;">related items</h5>
 
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* [[1 Fermion summation formula - quasi-particle interpretation|Boson and Fermion summation form]]<br>
 
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* [[asymptotic analysis of basic hypergeometric series]]<br>
 
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* [[quantum groups|Quantum groups]]<br>
 
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* [[Kashaev's volume conjecture|Kashaev's volume Conjecture]]<br>
 
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<h5>expositions</h5>
 
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* [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, 2011
 
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* [http://www.birs.ca/events/2010/5-day-workshops/10w5069/videos Quantum dilogarithm identities from quiver mutations], video of a talk given at Banff, September 9, 2010.
 
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<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>
 
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* Keller, http://arxiv.org/abs/1102.4148
 
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* Kashaev, http://arxiv.org/abs/1104.4630
 

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.


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 \(Q=b+b^{-1}\)


related items


computational resource

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'quantum'}, {'LEMMA': 'dilogarithm'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Quantum_dilogarithm&oldid=51912"