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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Imamura Yosuke
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue1-2(H119A) Fri1-2(H119A)
- Group
- -
- Course number
- PHY.Q434
- Credits
- 2
- Academic year
- 2016
- Offered quarter
- 3Q
- Syllabus updated
- 2016/12/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
The first half explains the structure of gauge theory, Higgs mechanism, path integral quantization of the gauge field, effective action and renormalization, and the renormalization group equation, covering the basics of quantum theory for gauge fields. The latter half covers basic topics chosen from supersymmetry, supergravity theory, super string theory, and conformal field theory.
Students are expected to learn the basic concepts and calculation methods for gauge theory.
Student learning outcomes
[Objectives]
In this course students will build on the basic topics of quantum field theory learned in Field Theory I to study path integral quantization of gauge theory, and methods for renormalization. Students will also acquire basic knowledge on recent advances in supersymmetry, supergravity, super string theory, and conformal field theory.
[Topics]
In the first half we will cover the structure of gauge theory, the Higgs mechanism, the path integral quantization of gauge fields, effective action and renormalization, renormalization group equations, and other basic problems of quantum gauge field theory. In the latter half we will cover supersymmetry, supergravity, super string theory, and conformal field theory.
Keywords
quantum field theory, gauge fields, Higgs mechanism, path integral, renormalization, supersymmetry, effective action
Competencies that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Gauge theory, Lie algebra | Understand the definition of Lie algebras. Check the gauge invariance of gauge field actions. |
| Class 2 | Spontaneous symmetry breaking and the Higgs mechanism | Calculate gauge particle masses |
| Class 3 | Path integral quantization (1). From quantum mechanics to bosonic fields. | Derive the path integral of a scalar field |
| Class 4 | Path integral quantization (2). Fermion fields, Fadeev-Popov method. | Derive the ghost action |
| Class 5 | Feynman rules and effective action. Quantization of gauge fields. | Derive the feynman rules for a gauge theory. |
| Class 6 | Dimensional regularization and renormalization | Carry out one loop integrals by using the dimensional reguralization |
| Class 7 | Renormalization group equations | Understand the meaning of renormalization group |
| Class 8 | Beta functions and asymptotic freedom | Understand the relation between the beta function and the asymptotic freedom |
| Class 9 | Supersymmetry, supersymmetry algebra, and BPS states | Confirm the supersymmetry algebra |
| Class 10 | Wess-Zumino model | Confirm the invariance of the Wess-Zumino action under the supersymmetry transformation |
| Class 11 | Supersymmetric Yang-Mills theory | Confirm the invariance of the action of a supersymmetric Yang-Mills theory under the supersymmetry transformation |
| Class 12 | Superspace | Derive the supersymmetry transformation rules by using superspace |
| Class 13 | Construction of Supersymmetric Yang-Mills theories in the superspace formalism | Derive the action by using superspace |
| Class 14 | Low energy effective action and holomorphy | Understand the meaning of the low energy effective action. |
| Class 15 | N=2 supersymmetric gauge theories | Understand the structure of multiplets in N=2 supersymmetric gauge theories |
Textbook(s)
None required
Reference books, course materials, etc.
Tobe indicated in the class
Assessment criteria and methods
Students' course score is based on a term paper
Related courses
- PHY.Q433 ： Field Theory I
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students should have completed Field Theory I (PHYQ433)
