"Non-unitary c(2,k+2) minimal models"의 두 판 사이의 차이

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<h5>introduction</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;">non-unitary <math>c(2,k+2)</math>''''''minimal models''''''</h5>
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*  central charge<br><math>c(2,k+2)=1-\frac{3k^2}{k+2}</math><br><math>k \geq 3</math>, odd<br>
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*  primary fields have conformal dimensions<br><math>h_j=-\frac{j(k-j)}{2(k+2)}</math>, <math>j\in \{0,1,\cdots,[k/2]\}</math><br>
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*  effective central charge<br><math>c_{eff}=\frac{k-1}{k+2}</math><br>
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*  dilogarithm identity<br><math>\sum_{i=1}^{[k/2]}L(\frac{\sin^2\frac{\pi}{k+2}}{\sin^2\frac{(i+1)\pi}{k+2}}})=\frac{k-1}{k+2}\cdot \frac{\pi^2}{6}</math><br>
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*  character functions<br><math>\chi_j(\tau)=q^{h_j-c/24}\prod_{n\neq 0,\pm(j+1)}(1-q^n)^{-1}</math><br>
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*  quantum dimension and there recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
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#  (*choose k for c (2,k+2) minimal model*)k := 11<br> (*define Rogers dilogarithm*)<br> L[x_] := PolyLog[2, x] + 1/2 Log[x] Log[1 - x]<br> (*quantum dimension for minimal models*)<br> f[k_, i_] := (Sin[Pi/(k + 2)]/Sin[(i + 1) Pi/(k + 2)])^2<br> (*effective central charge*)<br> g[k_] := (k*Pi^2)/(2 (k + 2))<br> (*compare the results*)<br> N[Sum[L[f[k, i]], {i, 1, k - 1}] + Pi^2/6, 10]<br> N[g[k], 10]<br> d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]<br> Table[{i, d[k, i]}, {i, 1, k}] // TableForm<br> Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,<br>    k}] // TableForm<br>
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<h5>history</h5>
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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<h5>related items</h5>
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* [[Andrews-Gordon identity]]
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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%;">encyclopedia</h5>
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* http://en.wikipedia.org/wiki/
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* http://www.scholarpedia.org/
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* http://www.proofwiki.org/wiki/
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
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<h5>books</h5>
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* [[2010년 books and articles]]<br>
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* http://gigapedia.info/1/
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* http://gigapedia.info/1/
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
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<h5>expositions</h5>
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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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* http://www.ams.org/mathscinet
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* http://www.zentralblatt-math.org/zmath/en/
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* http://arxiv.org/
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* http://www.pdf-search.org/
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* http://pythagoras0.springnote.com/
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
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* http://dx.doi.org/
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<h5>question and answers(Math Overflow)</h5>
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* http://mathoverflow.net/search?q=
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* http://mathoverflow.net/search?q=
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<h5>blogs</h5>
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*  구글 블로그 검색<br>
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**  http://blogsearch.google.com/blogsearch?q=<br>
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** http://blogsearch.google.com/blogsearch?q=
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* http://ncatlab.org/nlab/show/HomePage
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<h5>experts on the field</h5>
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* http://arxiv.org/
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<h5>links</h5>
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
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* http://functions.wolfram.com/

2010년 9월 24일 (금) 00:46 판

introduction

 

 

non-unitary \(c(2,k+2)\)'minimal models'
  • central charge
    \(c(2,k+2)=1-\frac{3k^2}{k+2}\)
    \(k \geq 3\), odd
  • primary fields have conformal dimensions
    \(h_j=-\frac{j(k-j)}{2(k+2)}\), \(j\in \{0,1,\cdots,[k/2]\}\)
  • effective central charge
    \(c_{eff}=\frac{k-1}{k+2}\)
  • dilogarithm identity
    \(\sum_{i=1}^{[k/2]}L(\frac{\sin^2\frac{\pi}{k+2}}{\sin^2\frac{(i+1)\pi}{k+2}}})=\frac{k-1}{k+2}\cdot \frac{\pi^2}{6}\)
  • character functions
    \(\chi_j(\tau)=q^{h_j-c/24}\prod_{n\neq 0,\pm(j+1)}(1-q^n)^{-1}\)
  • quantum dimension and there recurrence relation
    \(d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}\) satisfies
    \(d_i^2=1+d_{i-1}d_{i+1}\) where \(d_0=1\), \(d_k=1\)

 

  1. (*choose k for c (2,k+2) minimal model*)k := 11
    (*define Rogers dilogarithm*)
    L[x_] := PolyLog[2, x] + 1/2 Log[x] Log[1 - x]
    (*quantum dimension for minimal models*)
    f[k_, i_] := (Sin[Pi/(k + 2)]/Sin[(i + 1) Pi/(k + 2)])^2
    (*effective central charge*)
    g[k_] := (k*Pi^2)/(2 (k + 2))
    (*compare the results*)
    N[Sum[L[f[k, i]], {i, 1, k - 1}] + Pi^2/6, 10]
    N[g[k], 10]
    d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]
    Table[{i, d[k, i]}, {i, 1, k}] // TableForm
    Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,
       k}] // TableForm

 

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

expositions

 

 

 

articles

 

 

 

question and answers(Math Overflow)

 

 

blogs

 

 

experts on the field

 

 

links
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