MMath&Phys Mathematics and Physics / Course details

Quantum Field Theory

Follow - Up Units

PHYS40682 - Gauge Theories

To understand the unifying framework of quantization of fundamental forces and particles in agreement with special relativity.

1. Preliminaries           (3 Lectures)
Classical Lagrangian Dynamics; Lagrangian Field Theory; Global and Local Symmetries; Noether's Theorem.

2. Canonical Quantization                        (4 lectures)
From Classical to Quantum Mechanics; Quantum Fields and Causality; Canonical Quantization of Scalar Field Theory; Complex Fields and Anti-Particles.

3. The S-Matrix in Quantum Field Theory                     (5  lectures)
Time Evolution of Quantum States and the S-Matrix; Feynman Propagator and Wick's Theorem; Transition Amplitudes and Feynman Rules; Particle Decays and Cross Sections; Unitarity and the Optical Theorem.

4. Quantum Electrodynamics        (6  lectures)
Dirac Spinors;  Quantization of the Fermion Field;  Gauge Symmetry;  Quantization of the Electromagnetic Field;  the Photon Propagator and Gauge Fixing;  Feynman Rules for Quantum Electrodynamics.

5. Renormalization                          (6 lectures)
Renormalizability; Dimensional Regularization, Renormalization of a Scalar Theory; Anomalous magnetic moment and the Lamb shift.

Feedback will be available on students’ individual written solutions to selected examples, which will be marked, and model answers will be issued.

Cheng, T. P. and Li, L. F. Gauge Theory of Elementary Particle Physics, Oxford  University
Press, 1984.
Mandl, F. and Shaw, G. Quantum Field Theory, Wiley, 1992.
Peskin, M. E. and Schroeder, D. V. Quantum Field Theory, Perseus Books Group, 1995.
Pokorski, S. Gauge Field Theories, Cambridge University Press, 2000, Second Edition.