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課程名稱 |
量子場論
Perturbative quantum field theory |
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開課學期 |
104-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
馬梓銘 |
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課號 |
MATH5020 |
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課程識別碼 |
221 U6780 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二8,9(15:30~17:20)星期三10(17:30~18:20) |
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上課地點 |
天數304天數304 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042MATH5020_QFT |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
http://www.math.ntu.edu.tw/courses/super_pages.php?ID=allcourses |
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課程目標 |
We plan to go through (part of) Costello's book : Renormalization and effective field theory, on the mathematical formulation of perturbative Quantum field theory. The goal is to give a brief idea on how the quantization using Feynman diagram and renormalization is defined mathematically, illustrated by examples such as scalar field theory, Chern-Simon theory etc. |
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課程要求 |
Students are required to do two presentations on related materials. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
1. Chern-Simon Perturbative theory I and II, S. Axelrod and I. M. Singer
2. Calabi-Yau geometry and higher genus Mirror symmetry, Si Li
3. BV quantization and algebraic index, R. E. Grady, Q. Li and S. Li
4. Convergence of Bogoliubov's method of Renormalization in Momentum space, W. Zimmermann
5. On overlapping subdivergences, Dirk Kreimer
6. Renormalization and Riemann-Hilbert problem I-II, A. Connes and Kreimer |
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參考書目 |
1. K. Costello : Renormalization and effective field theory
2. Si Li's Lecture notes : Introduction to perturbative quantum field theory and
geometric applications
3. Notes on locally convex topological vector spaces, J. L. Taylor |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Presentation 1 |
50% |
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2. |
Presentation 2 |
50% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/23, 2/25 |
Introduction : Motivation from quantum mechanics |
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第2週 |
3/01,3/03 |
A finite dimensional toy model |
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第3週 |
3/08,3/10 |
First example of UV divergence : phi^4 theory |
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第4週 |
3/15,3/17 |
Heat kernel and asymptotic of graph integral |
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第5週 |
3/22,3/24 |
Construction of counter terms : Examples |
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第6週 |
3/29,3/31 |
Construction of local counter terms |
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第7週 |
4/05,4/07 |
No class this week |
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第8週 |
4/12,4/14 |
Definition of Scalar field theory and the Main theorem |
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第9週 |
4/19,4/21 |
BV construction in finite dimensional |
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第10週 |
4/26,4/28 |
Supermanifold and Berezinian integration |
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第11週 |
5/03,5/05 |
BV quantization in infinite dimensional |
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第12週 |
5/10,5/12 |
Obstruction theory in quantization |
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第13週 |
5/17,5/19 |
Local functionals and Jet bundles |
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第14週 |
5/24,5/26 |
Sheaf of theories and homotopy of theories |
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第15週 |
5/31,6/02 |
Quantum Observables and Factorization algebra |
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第16週 |
6/07,6/09 |
Presentation 1 |
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第17週 |
6/14,6/16 |
Presentation 2 |
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