2019年度夏学期 場の量子論 I
[学部4年生 + 大学院 共通講義]
2019 S-semester, Quantum Field Theory I
[common course for undergraduate and graduate students]
担当：浜口幸一（ホームページ）
Instructor: Koichi Hamaguchi (homepage)
お知らせ。Announcents
[Last updated: August 8.]
- レポートの問題(d-5)を一部修正しました。（代数閉じますね。複数の学生さんがレポートで指摘して下さいました。ありがとうございます。） (8/8.).
The problem (d-5) is partially corrected. (The algebra is closed. A couple of students pointed it out in the report. Thanks!) (August 8.)
- 講義ノートを最後までアップしました (6/25). 少しタイポを修正しました (7/25).
The whole lecture note is uploaded (June 25). Some typos corrected (July 25).
- レポート問題[c,d]をアップしました。(5/14)
The report problems [c,d] are uploaded. (May 14.)
- 初日の講義ノートとレポート問題[a,b]をアップしました。(4/8)
The lecture note on the first day and the report problems [a,b] are uploaded. (Apr. 8.)
- ページ作りました。(2/12)
This page is uploaded. (Feb. 12.)
- 板書は英語、話すのは日本語で行う予定です。（初回に希望を聞きます。）
I plan to speak mainly in Japanese and write mainly in English (on the blackboard).
I will ask your preference in the first class.
- 成績はレポート（複数回）で評価します。
Grades are given based on the scores of the homework problems.
- 前提知識として、量子力学と特殊相対論の基礎を仮定して講義をします。
Prerequisites for this lecture: basics of quantum mechanics and special relativity.
毎週火曜２限(10:25-12:10), 理学部1号館、207号室
Tuesday 10:25-12:10, room 207, Faculty of Science Bldg.1.
Apr. 9, 16, 23,
May 7, 14, 21, 28,
June 11, 18, 25, (no class on June 4)
July 2, 9, 23. (no class on July 16. We may have an additional class on July 30.)
レポート。Homework Problems
QFT_2019_report1.pdf
QFT_2019_report2.pdf
講義ノート。Lecture notes
QFT_2019.pdf
講義内容。Contents
(Note: It is a tentative plan, and will be updated every week once the lecture course starts.)
- Introduction
- about this lecture (Language, Web page, Schedule, Grades,...) [Apr.9]
- 1.1. Course objective and Plan [Apr.9]
- 1.2. Quantum Mechanics and Quantum Field Theory [Apr.9]
- 1.3. Notation and convention [Apr.9]
- 1.4. Hilbert space and Hamiltonian of (infinitely) many particles [Apr.9]
- Free Scalar (spin 0) Field
- 2.1. Lagrangian and Canonical Quantization of Real Scalar Field [Apr.16]
- 2.2. Equation of Motion (EOM) [Apr.16]
- 2.3. Solution of the EOM [Apr.16]
- 2.4. Commutation relations of a and a† [Apr.16]
- 2.5. a† and a are the creation and annihilation operators [Apr.23]
- 2.6. Vacuum state, one-particle state and n-particle state [Apr.23]
- Lorentz transformation, Lorentz group and its representations
- 3.1. Lorentz transformation of coordinates [Apr.23]
- 3.2. Infinitesimal Lorentz transformation and generators of Lorentz group (in the 4-vector basis) [May 7]
- 3.A. Other (disconnected) Lorentz transformations [May 7]
- 3.3. Lorentz transformation of scalar field [May 7, 14]
- 3.4. Lorentz transformations of other fields, and representations of Lorentz group [May 14, 21]
- 3.5. Spinor Fields [May 21]
- 3.6. Spinor bilinears [May 21, 28]
- Free Fermion (spin 1/2) Field
- 4.1. Lagrangian [May 28]
- 4.2. Dirac equation and its solution [May 28, June 11]
- 4.3. Quantization of Dirac field [June 11, 18]
- Interacting Scalar Field
- 5.1. Outline: what we will learn [June 18]
- 5.2. S-matrix, amplitude M ==> observables (σ and Γ) [June 18, 25]
- 5.3. Interacting Scalar Field: Lagrangian and Quantization [June 25]
- 5.4. What is φ(x)? [June 25, July 2]
- 5.5. In/out states and the LSZ Reduction Formula [June 25, July 2]
- 5.6. Heisenberg field and Interactin picture field [July 2]
- 5.7. a and a† (again) [July 2]
- 5.8. <0| T( φ(x) ...) |0> =? [July 9]
- 5.9. Wick's theorem [July 9]
- 5.10. Summary, Feynman rules, examples [July 23]
特定の教科書・参考書はありませんが、講義ノートを作る際に参考にした本をいくつかあげておきます。
This course is not based on a specific textbook, but I often refer to the following textbooks during preparing the lecture note.
- M. Srednicki, Quantum Field Theory.
- M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory.
- M. D. Schwartz, Quantum Field Theory and the Standard Model.
- S. Weinberg, The Quantum Theory of Fields volume I.
- 「ゲージ場の量子論 I」九後汰一郎、培風館.
- 「場の量子論」坂井典佑、裳華房.
浜口幸一（講義のページ／ホームページ）
Koichi Hamaguchi：homepage
http://www-hep.phys.s.u-tokyo.ac.jp/~hama/lectures/2019_QFT.html