MATH425: Quantum Field Theory

These are the materials for the MATH425 Quantum Field Theory course in Session 2025-26 at the Department of Mathematical Sciences of the University of Liverpool.

The material is strongly based on previous iterations of the course by Dr Juri Smirnov and Prof Martin Gorbahn.

Welcome

My name is Yannick, and I'm a Lecturer in Theoretical Physics at UoL, with a research focus on precision QED.

My office is on the first floor in theoretical physics wing. Nr. 105, and my email is: yannick.ulrich@liverpool.ac.uk.

I'm delighted to explore with you this exciting topic of fundamental theoretical physics.

Lecture materials

You can find the up-to-date lecture notes on my website as a pdf or a screenreader- and mobile-friendly web document. If you find typos or mistakes, please report them either per email or on gitlab.

The notes contain small exercises you can attempt either at home or during the lecture as well as further reading that is either marked with a grey background (pdf) or a foldable section (web document). This material is not examinable but it might provide you with some background knowledge and context.

The Mathematica notebook for the calculation of e^-e⁺→μ^-μ⁺ can be found here and viewed here.

Class times

Our class times are:

• Tuesday, 9am - 11am
• Thursday, 9am - 11am

The room allocation has changed and is now

• On most Tuesdays, we will be Mathematical Sciences 211 (Whittaker Room)

• On most Thursdays, we will be in Mathematical Sciences 105

• On 2 Dec and 9 Dec, we will instead be in Mathematical Sciences G16 (ground floor of the Theoretical Physics Wing).

I will send announcements for the changed rooms the day before but please make sure to check your timetable!

The 4h of contact time each week will be spend with a hybrid combination of lecture and tutorials where we will consider small derivations together.

Office hours

My office hours will be

• Monday, 2:30pm - 4:30pm (in-person or zoom)
• flexibly by appointment

You are welcome to ask questions at any time via email or preferably the Canvas Discussion page so that your peers may benefit from them. If you prefer, you can ask anonymously as well.

Assessment

There will be three assessed homework assignments (10%, 20%, 20%) and a final 90min exam (50%).

• The first homework, MATH425.3, will be due end of Week 4, i.e. 17 October, and be 20% of the final grade. You can find the sheet and solution here and here.
• The second homework, MATH425.4, will be due end of Week 9, i.e. 21 November, and be 10% of the final grade
• The third homework, MATH425.2, will be due end of Week 12, i.e. 12 December, and will be 20% of the final grade

The homework assignments and a mock exam will be shared in due course.

Exam

This year's QFT exam, MATH425.1, will be partially open book to avoid rote memorisation, thereby making it more authentic. You will be allowed to bring one A4 pieces of paper containing hand- or machine written notes. You may collaborate in the writing of these notes and I will share some guidance later in the year.

Note: If you have accessibility requirements related to this, please get in touch and we will come to an equitable solution.

Reading suggestions

We will mostly follow An Introduction to Quantum Field Theory by Michael Peskin and Daniel Schroeder. You can get an ebook or physical from the library.

Further suggested reading include

• Quantum Field Theory and the Standard Model by Matthew Schwartz. A good introductory book that follows a different approach to the same goal.

• Quantum Field Theory by Claude Itzykson and Jean-Bernad Zuber. An excellent reference book but less well suited as an introduction.