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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Yamaguchi Masahide
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-6() Thr5-6()
- Group
- -
- Course number
- PHY.Q433
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 2Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
Students will study quantization methods in interaction-free fields for Klein-Gordon fields, Dirac fields, and electromagnetic fields. Using canonical formalism, we will then introduce interaction, deriving Feynman rules, which are rules of operation, in order to make perturbation theoretical calculations. Using these, we will calculate the scattering cross-section measured in experiments, and the decay rate of unstable particles, finding that the measured values are replicated.
Quantum field theory deals with infinite degrees of freedom, fusing relativity and quantum theory.
Students in this course will learn the basics of quantum field theory, with an eye towards applications for high-energy physics and condensed matter physics.
Student learning outcomes
[Objectives]
Students in this course will study quantum field theory, the fundamental tool for representing the behavior of elementary particles, in particular relative quantum field theory. By calculating scattering amplitude using Feynman rules, students will be able to calculate the physical quantity of scattering cross-sections, etc.
[Topics]
We will learn about the properties of the responding field and techniques of quantization for scalar particles, fermion particles, and photons that appear in the theory of elementary particles. Students will derive Feynman rules in order to calculate the interaction between elementary particles, and use them to calculate the interaction between elementary particles with perturbation theory, learning techniques for calculating actually measured scattering cross-sections, decay rates, etc.
Keywords
Quantum Field Theory, Klein-Gordon field, Dirac field, electromagnetic field, Feynman rules, perturbation theory
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Lectures will be given in English.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | States in the quantum field theory | Explain how states in the quantum field theory are described. |
| Class 2 | Field operators | Explain what field operators are. |
| Class 3 | Klein-Gordon fields | Quantize a Klein-Gordon field and construct the Fock space. |
| Class 4 | Symmetries in the Klein-Gordon theory | Explain symmetries in the Klein-Gordon theory and the corresponding conservation law. |
| Class 5 | Interactions | Solve a few examples of toy models with interactions. |
| Class 6 | Asymptotic states | Explain what asymptotic states are. |
| Class 7 | Perturbative expansion | Draw Feynman diagrams for a few scattering processes. |
| Class 8 | Feynman rules | Write down the scattering amplitudes for a few examples of processes. |
| Class 9 | Scattering cross sections and decay rates. | Calculate the decay rate of the process from a scalar particle into two scalar particles. |
| Class 10 | Fermions | Explain what Grassmann numbers are. |
| Class 11 | Quantization of Dirac fields | Explain how electrons and positrons arise in the quantization of the Dirac field. |
| Class 12 | Symmetries of Dirac fields | Determine the transformation of a Dirac field under the charge conjugation. |
| Class 13 | Electromagnetic field | Carry out the canonical quantization of the electromagnetic field. |
| Class 14 | Feynman rules for the electromagnetic field | Write down the scattering amplitude of a process with electromagnetic interaction. |
Out-of-Class Study Time (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 specified
Reference books, course materials, etc.
specified during the course
Assessment criteria and methods
evaluated by exercise problems or final exam.
Related courses
- PHY.Q331 ： Relativistic Quantum Mechanics
- PHY.Q434 ： Field Theory II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
none specified
