2023 Faculty Courses School of Science Department of Physics Graduate major in Physics
Advanced Special Lectures in Physics XLIX
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Minoru Eto
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive
- Class
- -
- Course Code
- PHY.P690
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
In this lecture, I will introduce various topological solitons which appear in vast areas of modern physics from theoretical/phenomenological particle physics, cosmology, nuclear physics, and condensed matter physics. The reason why the topological solitons appear in such a wide range of physics is that they would be created as a result of spontaneous symmetry breaking that is independent of energy scales and details of systems.
Based mainly on relativistic field theories, I will explain what kind of topological solitons exist and what kind of properties they have according to the dimension of spacetime, symmetry, and field contents, and so on.
I will start with giving some theoretical basics such as topological invariants and homotopy groups, then I will explain how to solve soliton equations both analytically and numerically. I will also tell you defect-type topological solitons and texture-type topological solitons. Also fermion zero modes localizing on solitons, and solitons in supersymemtric theories will be explained.
For recent topics, I will choose hybrid topological solitons, fractional quantum vortices in multi component BECs, and chiral soliton lattices in QCD.
Course description and aims
The doctor course students are expected to fully understand the contents at the advanced level.
The students are expected to solve the advanced problems provided by the lecturer.
Keywords
symmetries, topology, topological solitons
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The lecture is given in a form of intensive course in Japanese.
12/11 (Mon) 13:00-17:30 (including breaks)
12/12 (Tue) 13:00-17:30 (including breaks)
12/13 (Wed) 13:00-17:30 (including breaks)
Place: TBA
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | spontaneous symmetry breaking and topological solitons | The lecturer will instruct during classes. |
| Class 2 | topological charge and homotopy groups | |
| Class 3 | defect-type topological solitons | |
| Class 4 | texture-type topological solitons | |
| Class 5 | fermion zero modes on solitons | |
| Class 6 | supersymmetry and topological solitons | |
| Class 7 | hybrid solitons | |
| Class 8 | fractional quantum vortices in multi component BECs | |
| Class 9 | chiral soliton lattice in QCD |
Study advice (preparation and review)
Textbook(s)
Classical theory of gauge fields: Valery Rubakov (Transrated by Stephen S. Wilson), Princeton University Press
Cosmic strings and other topological defects: A. Vilenkin and E.P.S. Shellard, Cambridge monographs on mathematical physics
Topological solitons: Nicholas Manton and Paul Sutcliffe, Cambridge monographs on mathematical physics
Classical solutions in quantum field theory: Erick J. Weinberg, Cambridge monographs on mathematical physics
Reference books, course materials, etc.
I will give my lecture note to participants.
Evaluation methods and criteria
Evaluated by questions and discussions during classes and a report related to lectures.
Related courses
- PHY.Q433 ： Field Theory I
- PHY.Q434 ： Field Theory II
- PHY.Q438 ： Quantum Mechanics of Many-Body Systems
Prerequisites
None.