2018年度夏学期 場の量子論 I
[学部4年生 + 大学院 共通講義]
2018 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: July 10.]
- 7/9, 23 の講義ノートをアップしました。(7/10)
The lecture note on July 9 and 23 is uploaded. (July 10)
- レポート問題２をアップしました。(5/7)
The homework (report) problems 2 are uploaded. (May 7)
- レポート問題１をアップしました。(4/16)
The homework (report) problems 1 are uploaded. (Apr. 16)
- 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 (more than one) 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.
毎週月曜２限(10:25-12:10), 理学部1号館、279号室
Monday 10:25-12:10, room 279, Faculty of Science Bldg.1.
Apr. 9, 16, 23,
May 7, 14, 21, 28,
June 4, 11, 18, 25,
July 2, 9, 23.
レポート。Homework Problems
QFT_2018_report1.pdf
QFT_2018_report2.pdf
講義ノート。Lecture notes
QFT_2018.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 objectives [Apr.9]
- 1.2. Quantum Mechanics and Quantum Field Theory [Apr.9]
- 1.3. Notation and convention [Apr.9]
- 1.4. Various fields [Apr.9]
- 1.5. Plan [Apr.9]
- 1.6. Hilbert space and Hamiltonian of (infinitely) many particles [Apr.9, 16]
- 1.7. About homework problems (and the grade) [Apr.16]
- Free Scalar (spin 0) Field
- 2.1. Lagrangian and Canonical Quantization of Real Scalar Field [Apr.16, 23]
- 2.2. Equation of Motion (EOM) [Apr.23]
- 2.3. Solution of the EOM [Apr.23]
- 2.4. Commutation relations of a and a† [Apr.23]
- 2.5. a† and a are the creation and annihilation operators [Apr.23, May.7]
- 2.6. Vacuum state, one-particle state and n-particle state [May.7]
- Lorentz transformation, Lorentz group and its representations
- 3.1. Lorentz transformation of coordinates [May.7, 14]
- 3.2. Infinitesimal Lorentz transformation and generators of Lorentz group (in the 4-vector basis) [May.14]
- 3.A. Other (disconnected) Lorentz transformations [May.14]
- 3.3. Lorentz transformation of scalar field [May.14]
- 3.4. Lorentz transformations of other fields, and representations of Lorentz group [May.21]
- 3.5. Spinor Fields [May.28]
- 3.6. Spinor bilinears [May.28, June 4]
- Free Fermion (spin 1/2) Field
- 4.1. Lagrangian [June 4]
- 4.2. Dirac equation and its solution [June 4, 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]
- 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 2, 9]
- 5.9. Wick's theorem [July 9]
- 5.10. Summary, Feynman rules, examples [July 9, 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/2018_QFT.html