Quantum dilogarithm

introduction

• 틀:수학노트
• 틀:수학노트
• http://arxiv.org/abs/hep-th/9611117

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

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/

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위키데이터

• ID : Q7269036