"Quantum dilogarithm"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
 
(사용자 2명의 중간 판 22개는 보이지 않습니다)
1번째 줄: 1번째 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;">introduction</h5>
+
==introduction==
  
−
* [http://pythagoras0.springnote.com/pages/7978406 양자 다이로그 함수(quantum dilogarithm)]
+
* {{수학노트|url=양자_다이로그_함수(quantum_dilogarithm)}}
 +
* {{수학노트|url=양자_다이로그_항등식_(quantum_dilogarithm_identities)}}
 +
* http://arxiv.org/abs/hep-th/9611117
  
−
 
 
  
−
 
+
==Knot and invariants from quantum dilogarithm==
  
−
<h5 style="margin: 0px; line-height: 2em;">근사 공식</h5>
+
* '''[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.
  
−
* <math>q=e^{-t}</math> and as the t goes 0 (i.e. as q goes to 1)<br>
+
* '''[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
  
−
<math>\sum_{n=0}^{\infty}\frac{q^{\frac{A}{2}n^2+cn}}{(q)_n}\sim\exp(\frac{C}{t})</math>
 
  
−
 
+
==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>
  
−
여기서 C는 [http://pythagoras0.springnote.com/pages/4855791 로저스 다이로그 함수 (Roger's dilogarithm)] 의 어떤 값에서의 합
 
  
−
 
+
==related items==
 +
* [[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/
  
−
<h5 style="margin: 0px; line-height: 2em;">Knot and invariants from quantum dilogarithm</h5>
 
  
−
* '''[Kashaev1995] '''<br>
+
[[분류:개인노트]]
−
*  a link invariant, depending on a positive integer parameter N, has been defined via three-dimensional interpretation of the cyclic quantum dilogarithm<br>
+
[[분류:Number theory and physics]]
−
*  The construction can be considered as an example of the simplicial (combinatorial) version of the three-dimensional TQFT<br>
+
[[분류:dilogarithm]]
−
*  this invariant is in fact a quantum generalization of the hyperbolic volume invariant.<br>
+
[[분류:migrate]]
−
*  It is possible that the simplicialTQFT, defined in terms of the cyclic quantum dilogarithm, can be associated with quantum 2 + 1-dimensional gravity.<br>
 
  
−
* '''[Kashaev1995]'''[http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm]<br>
+
==메타데이터==
−
** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418
+
===위키데이터===
−
 
+
* ID :  [https://www.wikidata.org/wiki/Q7269036 Q7269036]
−
 
+
===Spacy 패턴 목록===
−
 
+
* [{'LOWER': 'quantum'}, {'LEMMA': 'dilogarithm'}]
−
 
 
−
 
 
−
 
 
−
 
 
−
<h5>quantum dilogarithm identities</h5>
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
<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>
 
−
 
 
−
 
 
−
 
 
−
<h5>expositions</h5>
 
−
 
 
−
* [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, 2011
 
−
* [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.
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
<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>
 
−
 
 
−
* Keller, http://arxiv.org/abs/1102.4148
 
−
 
 
−
* Kashaev, http://arxiv.org/abs/1104.4630
 

2021년 2월 17일 (수) 03:08 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"