Topics of solvable lattice models and conformal field theories
Several topics (spin chains, Bethe Ansatz, Gaudin models, WZW models and their relations etc.) in the theory of solvable lattice models and conformal field theories are discussed. Knowledge on quantum mechanics and statistical mechanics will help understanding but it is not indispensable, as we shall start from the very short review on them and put emphasis on mathematical aspects. We mainly focus on so-called "rational models", but if time permits, "elliptic models" might be discussed.
讲师
日期
2026年09月15日 至 2027年01月05日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 14:20 - 16:55 | Shuangqing | - | - | - |
修课要求
Linear algebra, complex analysis. Knowledge on physics is welcome, but not indispensable.
课程大纲
We shall discuss following topics, but not strictly constrained to this list.
1. Review on quantum mechanics
2. Spin chain
3. Review of classical statistical mechanics
4. Vertex model and transfer matrix
5. 6-vertex models and spin chan models
6. Bethe Ansatz for the XXX model
7. Gaudin model
8. WZW model.
9. Critical level limit of WZW model and Gaudin model.
10. Wakimoto modules and Bethe Ansatz.
11. Reviews of elliptic functions.
12. The XYZ spin chain, the 8-vertex model and their Bethe Ansatz.
1. Review on quantum mechanics
2. Spin chain
3. Review of classical statistical mechanics
4. Vertex model and transfer matrix
5. 6-vertex models and spin chan models
6. Bethe Ansatz for the XXX model
7. Gaudin model
8. WZW model.
9. Critical level limit of WZW model and Gaudin model.
10. Wakimoto modules and Bethe Ansatz.
11. Reviews of elliptic functions.
12. The XYZ spin chain, the 8-vertex model and their Bethe Ansatz.
参考资料
R. J. Baxter: Exactly solved models in statistical mechanics.
B.Feigin, E.Frenkel, N.Reshetikhin: Gaudin model, Bethe Ansatz and critical level, Comm. Math. Phys. 166 (1994), 27–62.
Jimbo, Michio; Miwa, Tetsuji: Algebraic analysis of solvable lattice models. CBMS Regional Conference Series in Mathematics, 85. American Mathematical Society, (1995).
L. A. Takhtajan, L.D. Faddeev: The quantum method of the inverse problem and the Heisenberg XYZ model, Uspekhi Mat. Nauk 34:5 (1979), 13–63, (in Russian); Russian Math. Surveys 34:5 (1979), 11–68, (English transl.).
B.Feigin, E.Frenkel, N.Reshetikhin: Gaudin model, Bethe Ansatz and critical level, Comm. Math. Phys. 166 (1994), 27–62.
Jimbo, Michio; Miwa, Tetsuji: Algebraic analysis of solvable lattice models. CBMS Regional Conference Series in Mathematics, 85. American Mathematical Society, (1995).
L. A. Takhtajan, L.D. Faddeev: The quantum method of the inverse problem and the Heisenberg XYZ model, Uspekhi Mat. Nauk 34:5 (1979), 13–63, (in Russian); Russian Math. Surveys 34:5 (1979), 11–68, (English transl.).
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Takashi Takebe 从事数学物理可积系统方向的研究。 2023年8月前，他在俄罗斯莫斯科国立研究大学高等经济学院数学系担任教授，并于2023年9月加入北京雁栖湖应用数学研究院任研究员一职。