Quantum Field Theory

Course Aim

To introduce students to basic concepts and techniques in relativistic quantum field theory.

Course Description

Learn quantum field theory from lectures and by working through classic and recent papers to follow developments in the field.  Progress from a reconsideration of basic concepts in quantum effects acting on electrons and other particles, through to Feynman rules and diagrams, and Weyl and Dirac spinors.  Develop these concepts into gauge theories, field quantization, symmetry breaking, and renormalization.  Finally consider quantum chromodynamics, gravity and nuclear forces, and possibilities to unified field theory including strings.  Confirm these findings through homework exercise sets and a final examination. Due to recent developments, an emphasis is placed on random matrices and knot theory, topological field theory, and applications to topological insulators.

Course Contents

1. An electron in a uniform electromagnetic field: Landau levels
2. Canonical Quantization
3. Antiparticles
4. Particle decay
5. Feynman rules and the S-matrix
6. Weyl and Dirac spinors
7. Gauge Theories
8. Quantization of the electromagnetic field
9. Symmetry breaking
10. Path integrals
11. Aharonov-Bohm effect
12. Renormalization
13. Quantum chromodynamics
14. Nuclear forces and Gravity
15. Field unification


Homework: 60%, Final Exam, 40%

Prerequisites or Prior Knowledge

Quantum Mechanics and B11 Classical Electrodynamics


E. Brezin, Introduction to statistical field theory (Cambridge University Press)

Reference Books

Quantum Field Theory, by Michio Kaku (1993) Oxford University Press.
An Introduction to Quantum Field Theory, by Peskin and Schroder (1995) Westview Press.
Gauge Theories in Particle Physics, Vol. I and II, by Aitchison and Hey (2004) Institute of Physics