量子場論(三)
Quantum Field Theory (III)
學期
106-1
學分
3
學分
當期課號
5435
永久課號
IOP5442
開課單位
物理研究所
授課教師
高崇文
類別
選修
上課時間表
| 節 | 週四 |
|---|---|
2 09:00–09:50 | 量子場論(三) SC429 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
概述
將介紹規範場包含其量子化再重整化以及其它相關議題 目標: 使學生具備處理規範場之能力從事各領域前沿研究
先修科目
修過量子場論(一)(二)或能利用路徑積分公式處理自旋0與1/2場之量子化導出其Feynman rules者
評分方式
出席50% 作業 50%
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | (A) Introduction to Chiral Gauge Theories (B) Euclidean Solutions (C) Wilson Loop |
| 第 2 週 | (A)Differential forms (B)Homotopy theory (c) Cohomology of Lie Group |
| 第 3 週 | (A) Hamiltonian Formalism of constrained system (B) Hamiltonian Formalism of Abelian Gauge theories (C) Hamiltonian Formalism of Non-Abelian Gauge theories |
| 第 4 週 | (A) Faddeev-Popov Gauge fixing (B) Equivalence between different gauges (C) Feynman rules of gauge theories |
| 第 5 週 | Renormalization of gauge Theories (I): One-loop diagrams (A) Vacuum Polarization (B) Fermion self-energy (C) Vertex correction |
| 第 6 週 | Renormalization of gauge Theories (II): RGE and EA of gauge theories (A) RG equation of Gauge Theories (B) Background Field Method (C) Effective action of gauge theories |
| 第 7 週 | Renormalization of gauge Theories (III): IR divergence and BPHZ method (A) IR divergence (B) BPHZ method (C) Application of BPHZ method |
| 第 8 週 | Application of QED (A) Anomalous magnetic moment g-2 (B) Lamb shift of hydrogen (C) Lamb shift of muon-hydrogen |
| 第 9 週 | Symmetry and renormalization (A) Ward-Takahashi identity (B) BRST transformation (C) Slavnov-Taylor identity |
| 第 10 週 | (A) Gribov ambiguity (B) Gribov-Zwanzinger action (C) Refined Gribov-Zwanzinger action |
| 第 11 週 | Chiral Anomaly (I) (A) Chiral anomaly in 2D QED (B) Triangle diagrams: Dimension regularization (C) Triangle diagrams: Dimension regularization |
| 第 12 週 | Chiral Anomaly (II) (A) Fujikawa approach: Cut-off regulator (B) Fujikawa approach: Zeta regularization (C) Chiral anomaly and index theorem |
| 第 13 週 | More about anomaly (A) Anomaly in chiral gauge theory (B) Wess-Zumino consistency condition (C) Trace anomaly |
| 第 14 週 | Soliton and vortex (A) One dimension soliton (B) Derrick’s theorem (C) Vortics |
| 第 15 週 | Monopole (A) Magnetic monopole (B) Homotopy group (C)‘tHooft-Polyakov monopole |
| 第 16 週 | Chern-Simons Theories (A) Introduction to Chern-Simons Theories (B) Canonical quantization of Chern-Simon Theories (C) Chern-Simons Vortices |
| 第 17 週 | Instantons(I) (A) Classical Yang-Mills instantons (B) WKB tunneling (C) Fermion on the instanton background |
| 第 18 週 | Instantons (II) ADHM consturction for SU(2) ADHM consturction for SU(N) ADHM construction in general |
教科書
教授整理之筆記
Office Hours
- 地點
- 辦公室
- 時間
- 星期四下午一到三點
- 聯絡方式
- e-mail: cwkao@cycu.edu.tw