Phys721 — Quantum Field Theory I

Purpose of this course

We will explore the quantization of fields, showing that the resulting theories prove capable of describing relativistic particle interactions. For a particular choice of fields, we'll show that a quantum version of electromagnetism, called Quantum Electrodynamics, can be constructed. In comparison to experiment, this proves to be the most numerically accurate theory ever built.

Class Schedule

Mondays and Wednesdays, 10.30am — 11.50am in Small Hall 235.

Office Hours

to be determined

Lecture Notes

I’ll post the lecture notes i'm working from on this website as we go along. Hopefully this means you can do less writing and be a bit more focussed during lecture time. Please let me know of any errors you spot in the notes.

Books

There are lots of good QFT texts. Here are some that i'm familiar with:

• Peskin & Schroeder An Introduction to Quantum Field Theory. Overall the best choice for this class.
• Mandl & Shaw Quantum Field Theory. Gentle, much emphasis on QED.
• Ryder Quantum Field Theory. Emphasizes path integral approach and scalar fields.
• Brown Quantum Field Theory. Somewhat formal, emphasises path integrals. Pleasingly thorough, but annoying space-time metric.
• Weinberg Quantum Theory of Fields, Vol 1. Rather more formal, but very complete. Idiosyncratic notation takes a lot of getting used to.
• Zee Quantum Field Theory in a Nutshell. Not really a textbook, but very easy to read.
• Aitchison & Hey Gauge Theories in Particle Physics. Two volume series, not really a QFT textbook, but very easy to read.

Problem Sets

There will be regular problem sets on the material we cover in lectures. These are a very important part of the course, almost certainly more important than listening to your lecturer waffle on. Sitting through lectures may make you feel like you have learned something, but you don’t really know until you try to use the techniques you think you have learned. The only way to become comfortable with the tools is through practice.

I intend the problem sets to be pedagogic, and in some cases will fill in important topics that we don't have time to cover in lectures. There will be one problem set roughly every week, with a few gaps.

I would strongly suggest that you should work on the problems first on your own, but if you remain stuck you can confer with your peers or get help from me. I furthermore would strongly suggest that you use search engines or AI tools as a last resort only after you've exhausted your own efforts, conferred with your peers, and asked me for help — the experience of finding your way to a solution is a powerful learning process, and shortcutting it can cost you in the long-term. In addition (as with any purported solution to a problem) you should check carefully that any AI-generated answer makes sense.

Anything you present in a solution must reflect your understanding at a level where if I asked you to explain it to me on the blackboard, you would be able to. Simply copying someone else's solution without understanding it would not meet this bar, and will be considered to be cheating.

Because I will (try to) provide solutions promptly (to help you understand anything you might have missed while the problems are still fresh in your mind), significant extensions to problem set deadlines will not be possible. If you need a short extension of a few hours, you may request it in advance of the deadline. Large-scale unexpected incidents can be handled individually, please get in touch by email and we will arrange some accommodation.

The problem sets and deadlines will be posted below.

Topics

• Canonical quantization of scalar, spinor and vector fields
• Interacting field theories and Feynman diagrams
• Scattering theory
• Quantum electrodynamics
• Introduction to radiative corrections, loop diagrams and renormalization

Grading

Problem Sets: 50%, Final Exam (take-home): 50%.

Lecture Notes

Problem Sets