2020 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)
- Yosuke Imamura
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-2 Tue (Zoom) / 1-2 Fri (Zoom)
- Class
- -
- Course Code
- PHY.Q434
- Number of credits
- 200
- Course offered
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
Symmetries in relativistic quantum field theories and their breaking are explained.
Global and local symmetries, continuous and discrete symmetries, and supersymmetry are studied.
Course description and aims
[Objectives]
In this course students will study path integral formulation of gauge fields and fermion fields, different kinds of symmetries and their applications.
[Topics]
We will cover discrete symmetries, Abelian and non-Abelian gauge symmetries, chiral symmetry, and supersymmetry.
Keywords
quantum field theory, symmetry, gauge fields, Higgs mechanism, 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 | Global symmetries and conservation laws | Understand the Noethers theorem in QFT. |
| Class 2 | Path integral formulation of fermions | Understand how to quantize fermion fields with path integral. |
| Class 3 | Discrete symmetries of Dirac fields | Understand the C and P transformation rules for Dirac fields |
| Class 4 | Time reversal symmetry and the CPT theorem | Confirm the CPT invariance of the action of scalar and Dirac fields. |
| Class 5 | Yang-Mills theory | Confirm the gauge invariance of the Yang-Mills action |
| Class 6 | Path integral of gauge fields | Derive the gauge fixed action |
| Class 7 | Anomaly in 2-dim QED | Quantize the fermion fields in 2-dim QED and calculate the chiral anomaly. |
| Class 8 | 1-loop calculation of anomaly | Perform one-loop calculation for chiral anomaly |
| Class 9 | Path integral and anomaly | Understand the relation between the 2d chiral anomaly and the index theorem |
| Class 10 | Topological aspects in anomaly | Understand the relation between instantons and anomaly. |
| Class 11 | Spontaneous symmetry breaking | Understand the Nambu-Goldstone's theorem. |
| Class 12 | Symmetry of QCD | Understand the symmetry of QCD |
| Class 13 | Supersymmetry | Check the supersymmetric invariance of the Wess-Zumino action. |
| Class 14 | Seiberg-Witten exact solution | Understand what the Seiberg-Witten solutions are. |
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
Students' course score is based on a term paper
Related courses
- PHY.Q433 ： Field Theory I
Prerequisites
Students should have completed Field Theory I (PHYQ433)