2024 Faculty Courses School of Science Department of Physics Graduate major in Physics
Field Theory II
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Katsushi Ito
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-2 Tue / 1-2 Fri
- Class
- -
- Course Code
- PHY.Q434
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Symmetries in relativistic quantum field theories and their breaking are explained.
Internal and spacetime symmetries, supersymmetry and conformal symmetry are studied.
Course description and aims
[Objectives]
In this course students will study path integral formulation of bosonic and fermionic fields, different kinds of symmetries and their applications.
[Topics]
We will cover chiral symmetry, conformal symmetry, supersymmetry etc. and related phenomena.
Keywords
quantum field theory, symmetry, anomaly , conformal symmetry, path integral, supersymmetry
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Only basic ideas and outline of calculations are given in the lecture, and detailed calculations are left for students.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Internal symmetries and conservation laws | Understand the Noethers theorem in QFT. |
| Class 2 | Spacetime symmetries and conservation laws | Understand the relation between spacetime symmetries and conservation laws. |
| Class 3 | Path integral | Understand a derivation of the path integral from the canonical formalism. |
| Class 4 | Ward identities | Understand a derivation of Ward identities |
| Class 5 | Chiral anomaly | Confirm the chiral symmetry is broken by a quantum anomaly. |
| Class 6 | Anomalies and index theorems | Understand a relation between anomalies and index theorems. |
| Class 7 | Spontaneous symmetry breaking | Understand the Nambu-Goldstone's theorem. |
| Class 8 | Renormalization groups | Carry out 1-loop calculation and derive a renormalization group equation. |
| Class 9 | Conformal symmetry | Confirm conformal transformation form a Lie algebra. |
| Class 10 | Weyl anomaly | Understand Weyl anomalies. |
| Class 11 | Hawking radiation. | Understand a derivation of the Hawking radiation. |
| Class 12 | AdS/CFT correspondence | Explain what the AdS/CFT correspondence is. |
| Class 13 | c-theorem and a-theorem | Explain the definitions of `c' and `a'. |
| Class 14 | Supersymmetry and its breaking | Understand a role of Witten index in supersymmetry breaking. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required
Reference books, course materials, etc.
Tobe indicated in the class
Evaluation methods and criteria
Comprehensive assessment based on a variety of in-class quizzes, etc.
Related courses
- PHY.Q433 ： Field Theory I
Prerequisites
Students should have completed Field Theory I (PHYQ433)