量子場論(三)
Quantum Field Theory (III)
學期
111-1
學分
3
學分
當期課號
536964
永久課號
SCIP30032
開課單位
物理研究所
授課教師
高崇文
校區
光復
類別
選修
上課時間表
| 節 | 週四 |
|---|---|
7 15:30–16:20 | 量子場論(三) SC159 3 節連堂 |
8 16:30–17:20 | |
9 17:30–18:20 |
* 根據陽明交大上課時間表所列
概述
介紹規範場論的諸主題,包含古典規範場論,迅時子,規範場的量子化,紅外發散規範場的再重整化,規範場的異常(ANOMALY)等。
先修科目
量子場論(一)(二)
評分方式
期末口試
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Local symmetry of Fermions Abliean Gauge theory induced from one flavor Fermion Strength of Field tensor and its Lagrangian Non-Abliean Gauge theory induced from many flavor Fermions Strength of Field tensor and its Lagrangian Chiral Gauge theory of one flavor Fermion Chiral Gauge theory of many flavor Fermion SU(N) Lie Algebra |
| 第 2 週 | Equation of motion of Gauge theories Dual strength of field tensor Gauge field coupling to an external current Why Euclidean space? Self dual and anti-self dual solution Instanton solution Cartan-Maurer form SO(N) gauge theories Sp(2n) gauge theories |
| 第 3 週 | Parallel transport Wilson Loop Plaquette Area Law Classical Abelian Chern-Simons theory Anyonic Quantum Mechanics C,P,T in 2+1 dim Fermion in 2+1 dim 2+1 dim Poincare algebra Classical non-Abelian Chern-Simons theory Gravity as Gauge theory: tetrad formalism Gravity as Gauge theory: torsion and curvature Gravity as Gauge theory: Einstein equation Gravity as Gauge theory: Couple to fermion and EM Gravity as Gauge theory: Killing equation |
| 第 4 週 | Differential forms:Introduction Abelian Gauge Theory in Differential forms Non-Ableian Gauge theory in Differential forms Gravity in Differential forms Complex Manifold Fiber Bundle Exact sequence of Fiber bundle |
| 第 5 週 | Introduction to Homotopy group Fundamental group Higher homotopy group Brouwer degree Boundary homomorphism Hopf mapping How to apply exact sequence of Fiber bundle to calculate Homotopy group Characteristic class of Fiber bundle Cohomology of Lie group Soliton in 1+1 dim ANO vortex in 2+1 dim O(3) sigma model and CP(1) model CP(N-1) model Dirac Magnetic Monopole |
| 第 6 週 | Magnetic monopole of Abelian Higgs model t'Hooft-Polyakov monopole Skymion WZW terms Instanton in QM Hamiltonian formalism of constrained system |
| 第 7 週 | Hamiltonian formalism of Abelian Gauge theory Hamiltonian formalism of Non-Abelian Gauge theory Faddeev-Popov method Ghost Feynman rules of Gauge theory in different gauges |
| 第 8 週 | Gribov ambiguity |
| 第 9 週 | Gribov region and no-pole condition Ghost and gluon propagators in Landau gauge Canonical quantization of Non-Abelian Gauge theory (I) : constraint and infinity |
| 第 10 週 | Canonical quantization of Non-Abelian Gauge theory (II) : equation of motions and constraints Infrared Divergence (I): One loop in QED |
| 第 11 週 | Infrared Divergence (II): All orders in QED Infrared Divergence (III) General theorems Analysis of UV divergence: degrees of superficial divergence One-Loop diagram: vacuum polarization |
| 第 12 週 | One-Loop diagram: Fermion self-energy One-Loop diagram:Vertex correction One-Loop diagram: g-2 and Lamb shift |
| 第 13 週 | Zinn-Just equation Proof of renormalizability of Non-Abelian Gauge theory |
| 第 14 週 | Background field method Background field gauge Beta function at one loop A4 term in BGM 1+1 Abelian Gauge theory with chiral fermion |
| 第 15 週 | point-splitting method 1+3 Abelian Gauge theory with chiral fermion Triangle diagrams: momentum shift Triangle diagrams: Pauli-Villiar regulator |
| 第 16 週 | Chiral Anomaly as the Jacobin: Cut-off Regulator Chiral Anomaly as the Jacobin: Zeta regularization Anomaly and index theorem Trace anomaly Non-Abelian anomaly Wess-Zumino consistency condition Bardeen form of Non-Abelian anomaly |
| 第 17 週 | Relevant and irrelevant anomaly Covariant and consistent anomaly cancellation of anomaly in the stand model Characteristic class and descent equations Wess-Zumino consistency condition and BRST Global anomaly |
教科書
Pierre Ramond: Field Theory: A modern Primer Steve Weinberg: The Quantum Theory of Fields II Stefan Pokorski” Gauge Field Theories Muta: QCD
Office Hours
- 時間
- 周四