Quantum Field Theory
Course Description
This is a graduate course on Quantum Field Theory (QFT).
QFT is an enormous subject and this course only gets you started. The goal is to understand QFT to the point that it becomes practical!
The choice of topics only reflects my personal interest and is biased towards applications in QCD. Along the way, we develop various analytical and numerical techniques in solving non-perturbative problems in field theory.
Here are some topics we explore:
(1) Elementary Particle Physics: Fermi’s Golden Rule, Feynman Diagrams, and Scattering Theory
(2) Symmetries and their spontaneous breaking
(3) Quantum Field Theory at zero and finite temperature
(4) Non-perturbative methods in QFT
Marking Scheme
0.6 assignments & projects + 0.4 exam
Aims
By the end of the course, the students will be able to:
- gain a deeper understanding of many body quantum mechanical systems
- follow research literatures and reviews
Textbooks
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Nuclear and High Energy Physics
-
Basic QFT
- Peskin and Schroeder, An Introduction to Quantum Field Theory
-
Many Body Theory
- Negele and Orland, Quantum Many-Particle Systems
- J. Kapusta and C. Gale, Finite-Temperature Field Theory: Principles and Applications
- A. Fetter and J.D. Walecka, Quantum Theory of Many Particle Systems
Topics
- Particle Physics for Babies
- The Standard Model of particle physics
- Gauge Theory: symmetry, charge and boson exchange
- Advanced Quantum Mechanics
- Angular Momenta
- Fermi Golden Rule
- scalar, fermions, and gauge fields
- vacuum energies
- important amplitudes in QED: discovery of quarks
- running couplings
- Bogoliubov transform and Quasi Particles
- Spectrum of Hadrons: SU(3) Flavor Symmetry and the Eight-Fold Way
- flavor symmetry
- color symmetry
- Constituent Quark Model
- Introduction to Functional Integrals
- 3 ways to QFT
- Z, W, and Gamma
- Master Equation for Symmetries
- Scattering and Unitarity
- kinematics and phase spaces
- optical theorem
- Topics in Nuclear Physics
- Liquid Drop Model
- Fermi Gas Model
- Relativistic Mean Field
- Finite Temperature Field Theory (optional)
- free bosons and fermions
- imaginary time formalism
Preparation and Help
The presentation of physics topics aims to be self-contained, but it is best to come prepared. You should be adept at quantum mechanics. Some knowledge of nuclear and high energy physics would be very helpful but not required. Some familiarity with numerical computation would be a big plus. The most important is the willingness to learn new stuffs. There is a lot to read.
For documentation of codes and works, use of latex and markdown is recommended.