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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Ito Katsushi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue1-2(H115) Fri1-2(H115)
- Group
- -
- Course number
- PHY.Q433
- Credits
- 2
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
First we will look back on how, in familiar electromagnetism, the diffusion of charged particles from an electromagnetic field was handled quantum mechanically. Then 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. Exercise problems related are provided after each lecture.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | fields and particles, second quantization, electromagnetic fields and photon | Understand necessity of fields and their quantization |
| Class 2 | Lagrangian in field theory | Understand Lagrangian in field theory |
| Class 3 | Symmetry and conservation law, Noether's theorem | Understand symmetry in field theory |
| Class 4 | quantization of Klein-Gordon fields | Understand quantization of Klein-Gordon field |
| Class 5 | Wick's theorem, propagator | Understand correlation functions of free scalar fields |
| Class 6 | Dirac spinors and the Dirac equations | Understand Dirac spinor and the Dirac equation |
| Class 7 | Dirac matrices and their properties | Understand Dirac matrices and their properties |
| Class 8 | quantization of Dirac fields | Understand quantization of Dirac fields |
| Class 9 | gauge symmetry, interaction terms in Lagrangian between electromagnetic fields and charged particle | Understand gauge symmetry and Lagrangian of fields interacting with electromagnetic fields |
| Class 10 | propagator of electromagnetic fields | Understand quantization of electromagnetic fields |
| Class 11 | scattering matrix | Understand scattering matrix |
| Class 12 | interaction picture representation | Understand interaction picture representation of scattering matrix |
| Class 13 | Derivation of Feynman rules by canonical formalism | Understand derivation of Feynman rules |
| Class 14 | calculation of 4 point scattering amplitudes | Understand method of calculation of 4 point scattering amplitudes |
| Class 15 | calculation of cross sections and decay rates | Understand calculation of cross sections and decay rates |
Textbook(s)
none specified
Reference books, course materials, etc.
specified during the course
Assessment criteria and methods
evaluated by exercise problems
Related courses
- PHY.Q331 ： Relativistic Quantum Mechanics
- PHY.Q434 ： Field Theory II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
none specified
