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2021　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.)
Tue1-2()  Fri1-2()  
Group
-
Course number
PHY.Q434
Credits
2
Academic year
2021
Offered quarter
3Q
Syllabus updated
2021/9/29
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.
Global and local symmetries, continuous and discrete symmetries, and supersymmetry are studied.

Student learning outcomes

[Objectives]
In this course students will study path integral formulation of gauge fields and fermion fields, different kinds of symmetries and their applications.
[Topics]
We will cover discrete symmetries, Abelian and non-Abelian gauge symmetries, chiral symmetry, and supersymmetry.

Keywords

quantum field theory, symmetry, gauge fields, Higgs mechanism, 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 Global symmetries and conservation laws Understand the Noethers theorem in QFT.
Class 2 Path integral formulation of fermions Understand how to quantize fermion fields with path integral.
Class 3 Discrete symmetries of Dirac fields Understand the C and P transformation rules for Dirac fields
Class 4 Time reversal symmetry and the CPT theorem Confirm the CPT invariance of the action of scalar and Dirac fields.
Class 5 Yang-Mills theory Confirm the gauge invariance of the Yang-Mills action
Class 6 Path integral of gauge fields Derive the gauge fixed action
Class 7 Anomaly in 2-dim QED Quantize the fermion fields in 2-dim QED and calculate the chiral anomaly.
Class 8 1-loop calculation of anomaly Perform one-loop calculation for chiral anomaly
Class 9 Path integral and anomaly Understand the relation between the 2d chiral anomaly and the index theorem
Class 10 Topological aspects in anomaly Understand the relation between instantons and anomaly.
Class 11 Spontaneous symmetry breaking Understand the Nambu-Goldstone's theorem.
Class 12 Symmetry of QCD Understand the symmetry of QCD
Class 13 Supersymmetry Check the supersymmetric invariance of the Wess-Zumino action.
Class 14 Seiberg-Witten exact solution Understand what the Seiberg-Witten solutions are.

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

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)

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