The first half explains the structure of gauge theory, Higgs mechanism, path integral quantization of the gauge field, effective action and renormalization, and the renormalization group equation, covering the basics of quantum theory for gauge fields. The latter half covers basic topics chosen from supersymmetry, supergravity theory, super string theory, and conformal field theory.
Students are expected to learn the basic concepts and calculation methods for gauge theory.
[Objectives]
In this course students will build on the basic topics of quantum field theory learned in Field Theory I to study path integral quantization of gauge theory, and methods for renormalization. Students will also acquire basic knowledge on recent advances in supersymmetry, supergravity, super string theory, and conformal field theory.
[Topics]
In the first half we will cover the structure of gauge theory, the Higgs mechanism, the path integral quantization of gauge fields, effective action and renormalization, renormalization group equations, and other basic problems of quantum gauge field theory. In the latter half we will cover supersymmetry, supergravity, super string theory, and conformal field theory.
quantum field theory, gauge fields, Higgs mechanism, path integral, renormalization, supersymmetry, effective action
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Only basic ideas and outline of calculations are given in the lecture, and detailed calculations are left for students.
Course schedule | Required learning | |
---|---|---|
Class 1 | Global symmetries and conservation laws | Understand the definition of Lie algebras and the Noethers theorem in QFT. |
Class 2 | Local symmetries and gauge fields | Understand how to localize the symmetry by introducing gauge fields. |
Class 3 | Yang-Mills theory | Check the gauge invariance of the Yang-Mills action. |
Class 4 | Gauge fixing and ghost fields | Derive the ghost action |
Class 5 | Effective action | Understand the definition and the meaning of the effective action. |
Class 6 | Anomalies | Calculate an anomaly in a simple example. |
Class 7 | Symmetry breaking | Calculate the mass of gauge fields in a system with broken gauge symmetry. |
Class 8 | Symmetries in QCD | Check the global symmetry of the QCD action. |
Class 9 | Running coupling constants | Calculate the energy dependence of coupling constant in a simple system. |
Class 10 | Renormalization group equation | Understand the meaning of renormalization group equations. |
Class 11 | Wess-Zumino-Witten action | Understand the physical meaning of the Wess-Zumino-Witten action. |
Class 12 | Electric-magnetic duality | Understand how the coupling constant is transformed under the electric-magnetic duality. |
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. |
Class 15 | Relation between field theories and string theory | Understand the relation between open strings and Yang-Mills fields. |
None required
Tobe indicated in the class
Students' course score is based on a term paper
Students should have completed Field Theory I (PHYQ433)