"Yang-Baxter equation (YBE)"의 두 판 사이의 차이
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| 13번째 줄: | 13번째 줄: | ||
* in the space of couplings a submanifold exists, such as that the transfer matrices corresponding to any two points P and P' on it commute<br> | * in the space of couplings a submanifold exists, such as that the transfer matrices corresponding to any two points P and P' on it commute<br> | ||
* characterized by a set of equations on the Boltzmann weights<br> | * characterized by a set of equations on the Boltzmann weights<br> | ||
| − | ** this set of equations is called the Yang Baxter equation<br> | + | ** this set of equations is called the Yang-Baxter equation<br> |
* solutions to Yang-Baxter equation can lead to a construction of integrable models<br> | * solutions to Yang-Baxter equation can lead to a construction of integrable models<br> | ||
| 25번째 줄: | 25번째 줄: | ||
* we need the trasfer matrices coming from different set of Boltzman weights commute <br> | * we need the trasfer matrices coming from different set of Boltzman weights commute <br> | ||
* partition function = trace of power of transfer matrices<br> | * partition function = trace of power of transfer matrices<br> | ||
| − | * so the | + | * so the problem of solving the model is reduced to the computation of this trace<br> |
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| + | * we make a matrix from the Boltzmann weights<br> | ||
| + | * if we can find an R-matrix, then it implies the existence of set of B<br> | ||
| + | * spectral parameters<br> | ||
| + | * anistropy parameters<br><br><br> | ||
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<h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">related items</h5> | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">related items</h5> | ||
2009년 8월 11일 (화) 11:48 판
introduction
- exact solvability of many models is explained by commuting transfer matrices
- manifestations of Yang-Baxter equation
- factorizable S-matrix
- factorizable S-matrix
- \(R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}\)
integrability of a model
- in the space of couplings a submanifold exists, such as that the transfer matrices corresponding to any two points P and P' on it commute
- characterized by a set of equations on the Boltzmann weights
- this set of equations is called the Yang-Baxter equation
- this set of equations is called the Yang-Baxter equation
- solutions to Yang-Baxter equation can lead to a construction of integrable models
transfer matrix
- transfer matrix is builtup from matrices of Boltzmann weights
- we need the trasfer matrices coming from different set of Boltzman weights commute
- partition function = trace of power of transfer matrices
- so the problem of solving the model is reduced to the computation of this trace
R-matrix
- we make a matrix from the Boltzmann weights
- if we can find an R-matrix, then it implies the existence of set of B
- spectral parameters
- anistropy parameters
Bethe ansatz
YBE for vertex models
- Yang-Baxter equation
- conditions satisfied by the Boltzmann weights of vertex models
표준적인 도서 및 추천도서
- 찾아볼 수학책
- Knots and physics
- Louis H. Kauffman
- Quantum Groups in Two-Dimensional Physics
- Yang-Baxter Equations, Conformal Invariance And Integrability In Statistical Mechanics And Field Theory
- http://gigapedia.info/1/knots+physics
- http://gigapedia.info/1/two-dimensional+physics
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
참고할만한 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Yang-Baxter
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(첨부파일로 올릴것)
블로그
- 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
- 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=
논문검색
- Integrable theories, Yang-Baxter algebras and quantum groups: An overview
- Yang-Baxter algebras, integrable theories and quantum groups
- H. J. De Vega
- Yang-Baxter algebras, integrable theories and Betre Ansatz
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- 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=