"Universal chiral partition function"의 두 판 사이의 차이
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| − | + | ==introduction== | |
* grand partition function for n species of right moving (chiral) particles with fugacities z<br> | * grand partition function for n species of right moving (chiral) particles with fugacities z<br> | ||
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| − | + | ==physical meaning== | |
<math>f_{A,B,C}(\tau)=\sum_{n\in \mathbb{Z}_{\geq 0}^r}\frac {q^{\frac{1}{2}n^{t}An+B^{t}\cdot n+C}} {(q)_{n_1}\cdots(q)_{n_r}}</math> | <math>f_{A,B,C}(\tau)=\sum_{n\in \mathbb{Z}_{\geq 0}^r}\frac {q^{\frac{1}{2}n^{t}An+B^{t}\cdot n+C}} {(q)_{n_1}\cdots(q)_{n_r}}</math> | ||
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| − | + | ==special cases== | |
* rank 1 case examples<br> | * rank 1 case examples<br> | ||
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| − | + | ==history== | |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 53번째 줄: | 53번째 줄: | ||
| − | + | ==related items== | |
* [[fractional and exclusion statistics]]<br> | * [[fractional and exclusion statistics]]<br> | ||
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| − | + | ==encyclopedia== | |
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
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| − | + | ==books== | |
| 87번째 줄: | 87번째 줄: | ||
| − | + | ==articles== | |
* [http://arxiv.org/abs/hep-th/9903176 Exclusion statistics in conformal field theory and the UCPF for WZW models]<br> | * [http://arxiv.org/abs/hep-th/9903176 Exclusion statistics in conformal field theory and the UCPF for WZW models]<br> | ||
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| − | + | ==question and answers(Math Overflow)== | |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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| − | + | ==blogs== | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
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| − | + | ==experts on the field== | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
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| − | + | ==links== | |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
2012년 10월 28일 (일) 18:12 판
introduction
- grand partition function for n species of right moving (chiral) particles with fugacities z
- N개의 보존 입자가 있고, 에너지의 단위를 \(\hbar\omega=1\)으로 하여, 에너지레벨이 \(E_0,E_1,E_2,\cdots\) 인 시스템을 생각하자.
N개의 입자가 있는 보존 시스템의 분배함수를 \(Z_B(N)\) 이라 두자.
큰 분배함수(grand partition function)는 \(Z_G=\sum_{n=0}^{\infty}Z_B(N)z^N\) 으로 쓸수 있다.
\(n_0,n_1,n_2,\cdots\) 은 각각 에너지가 \(E_0,E_1,E_2,\cdots\)인 입자의 수라고 하자.
\(Z_B(N)=\sum_{\sum n_r=N}\exp(-\beta\sum_{r}n_r E_r)\) 이므로,
\(Z_G=\sum_{N=0}^{\infty}Z_B(N)z^N=\sum_{N=0}^{\infty} \sum_{\sum n_r=N}\exp(-\beta\sum_{r}n_r E_r)z^N\)
\(=\prod_{r=0}^{\infty}\sum_{n_r=0}^{\infty} (ze^{-\beta E_r})^{n_r}=\prod_{r=0}\frac{1}{1-ze^{-\beta E_r}}\)
physical meaning
\(f_{A,B,C}(\tau)=\sum_{n\in \mathbb{Z}_{\geq 0}^r}\frac {q^{\frac{1}{2}n^{t}An+B^{t}\cdot n+C}} {(q)_{n_1}\cdots(q)_{n_r}}\)
A: energy shift due to interaction
B : energy shift due to (global) statistics
C : ground state Casimir energy
special cases
- rank 1 case examples
- Berkovich1998 and Wu's paper
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- Exclusion statistics in conformal field theory and the UCPF for WZW models
- Peter Bouwknegt, Leung Chim, David Ridout, 1999
- Comment on the paper ``The universal chiral partition function for exclusion statistics
- K. Schoutens (University of Amsterdam)
- K. Schoutens (University of Amsterdam)
- Berkovich, A., 와/과B. M McCoy. 1998. “The universal chiral partition function for exclusion statistics”. hep-th/9808013 (8월 4). http://arxiv.org/abs/hep-th/9808013
- Statistical distribution for generalized ideal gas of fractional-statistics particles
- Y.S. Wu,, Phys. Rev. Letts. 73 (1994) 922
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[1]
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
experts on the field