Universal chiral partition function
imported>Pythagoras0님의 2012년 10월 28일 (일) 15:57 판 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로)
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==
related items==
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=
4909919
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)
- 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/
- Peter Bouwknegt, Leung Chim, David Ridout, 1999
- K. Schoutens (University of Amsterdam)
- Y.S. Wu,, Phys. Rev. Letts. 73 (1994) 922