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2024　Field Theory II

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Academic unit or major
Graduate major in Physics
Instructor(s)
Ito Katsushi 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
-
Group
-
Course number
PHY.Q434
Credits
2
Academic year
2024
Offered quarter
3Q
Syllabus updated
2024/3/14
Lecture notes updated
-
Language used
English
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Course description and aims

Symmetries in relativistic quantum field theories and their breaking are explained.
Internal and spacetime symmetries, supersymmetry and conformal symmetry are studied.

Student learning outcomes

[Objectives]
In this course students will study path integral formulation of bosonic and fermionic fields, different kinds of symmetries and their applications.
[Topics]
We will cover chiral symmetry, conformal symmetry, supersymmetry etc. and related phenomena.

Keywords

quantum field theory, symmetry, anomaly , conformal symmetry, path integral, supersymmetry

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 Internal symmetries and conservation laws Understand the Noethers theorem in QFT.
Class 2 Spacetime symmetries and conservation laws Understand the relation between spacetime symmetries and conservation laws.
Class 3 Path integral Understand a derivation of the path integral from the canonical formalism.
Class 4 Ward identities Understand a derivation of Ward identities
Class 5 Chiral anomaly Confirm the chiral symmetry is broken by a quantum anomaly.
Class 6 Anomalies and index theorems Understand a relation between anomalies and index theorems.
Class 7 Spontaneous symmetry breaking Understand the Nambu-Goldstone's theorem.
Class 8 Renormalization groups Carry out 1-loop calculation and derive a renormalization group equation.
Class 9 Conformal symmetry Confirm conformal transformation form a Lie algebra.
Class 10 Weyl anomaly Understand Weyl anomalies.
Class 11 Hawking radiation. Understand a derivation of the Hawking radiation.
Class 12 AdS/CFT correspondence Explain what the AdS/CFT correspondence is.
Class 13 c-theorem and a-theorem Explain the definitions of `c' and `a'.
Class 14 Supersymmetry and its breaking Understand a role of Witten index in supersymmetry breaking.

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 required

Reference books, course materials, etc.

Tobe indicated in the class

Assessment criteria and methods

Comprehensive assessment based on a variety of in-class quizzes, etc.

Related courses

  • PHY.Q433 ： Field Theory I

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students should have completed Field Theory I (PHYQ433)

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