(Course description last updated for academic year 2014-15).
Prerequisites

This course requires a high-level of mathematical facility.

Learning Outcomes and Assessment

Quantum field theory is the language in which much of modern physics is formulated. It provides a synthesis of quantum theory and special relativity and offers a mathematical framework in which to describe many particle systems. This course is an introduction to quantum field theory using the canonical quantization approach in which classical degrees of freedom are replaced by operators.

 

Synopsis

Classical Field Theory: Lagrangian field theory, Symmetries, Noether’s theorem and conserved currents, Hamiltonian field theory.

Canonical Quantization: The Klein-Gordon equation, Free quantum fields, Vacuum energy, Emergence of particles, The Heisenberg picture, Causality and propagators, Applications, Non-relativistic field theory.

Interacting Fields: Types of interaction, The interaction picture, Dyson’s formula, Scattering, Wick’s theorem, Feynman diagrams and Feynman rules, Amplitudes, Green’s functions, Connected diagrams and vacuum bubbles.

The Dirac Equation: The Lorentz group, Clifford algebras, Spinor representation, The Dirac Lagrangian, Chiral spinors, The Weyl equation, Symmetries and currents.

Quantizing the Dirac Field: A glimpse at the spin-statistics theorem, Fermionic quantization, Fermi-Dirac statistics, Propagators, Particles and anti-particles, Dirac’s hole interpretation.

Quantum Electrodynamics: Gauge invariance, Quantization, QED, Lorentz invariant propagators, Feynman rules, Processes in QED involving electrons, positrons and photons.

BOOKS

An Introduction to Quantum Field Theory, Peskin M E and Schroeder D V (Addison-Wesley 1996) A very clear and comprehensive book. To a large extent, the course will follow the first section of this book.

Quantum Field Theory, Ryder L H (2nd edn CUP 1996) An elementary text covering most of the material in this course.

Quantum Field Theory in a Nutshell, Zee, A (Princeton University Press 2003). A charming book, where the emphasis is placed on physical understanding and the author isn’t afraid to hide the ugly truth when necessary. However, Zee primarily uses the path integral approach which we won’t cover in this course.

The Quantum Theory of Fields, Vol 1. Weinberg S (CUP 1995). Weinberg takes a unique route through the subject, focussing initially on particles rather than fields.

There is a course webpage with lecture notes at:http://www.damtp.cam.ac.uk/user/tong/qft.html

Course section:

Other Information

Staff
Dr Alejandra Castro-AnichLecturer