This web site is for the QFT course phi4propagator1PIexamplegiven in the academic year 18-19 (lecturer Tim Evans). From Autumn 2019 onwards, the course will be given by Toby Wiseman. While much of the basic content is likely to be similar, there will be changes and some of these could be significant.

‌26 hours of lectures, Rapid Feedback classes (see below) every two weeks plus two office hours each week, all during the Autumn term.  Seven problem sheets will be handed out but are not assessed, along with numerous additional handouts. A final revision lecture and exam office hours will be given in the summer term.

The physics undergraduate lecture schedule on the undergraduate website is the definitive timetable for this course, not the MSc timetable available elsewhere. 

Recent Updates (27/5/19)

(27/5/19) Feedback on the summer 2019 exam will be posted automatically on Friday 28th June at 18:00.


General Information for Autumn 2018 Course

  • Summary of key facts (5/10/18) (office hour times corrected) provides general overview and guidance on the prerequisites and knowledge needed for this course. Checkout PS1 (11/10/17) (Problem Sheet 1) as that is a good test to see if you are ready for the course.
  • The Syllabus for the Autumn 2018 QFT course‌ is available.
  • There is normally an early rapid feedback in the second week of Autumn term on Q2 and Q4 of PS1 (11/10/17).  This problem sheet does not draw on material from the lecture course but it illustrates the level of algebraic manipulations of annihilation and creation operators needed for the course. The problem sheet acts as a warm up for the course and can be done before the course starts. For written feedback hand in by noon, Monday before the class, as detailed under the rapid feedback section of this website.
  • The library has a nice version of my QFT bibliography with links to the actual texts. Information from my Bibliography (5/5/18) is largely duplicated there except for my comments on each text.


Below is a rough outline of the course. A detailed Syllabus for the Autumn 2018 QFT course is online and no major changes are expected in 2018 from the 2017 course. Check my Bibliography (5/5/18) with more detailed comments on a range of books. 

Introduction. (1 lecture) Basic aims and ideas of field theory. Types of field and relationship to symmetries (relativistic, non-relativistic symmetry and other particle symmetries).

Classical Field Theory and Scalar Fields. (5 lectures) Lagrangian and Hamiltonian descriptions of field theory. Linearity and interactions. Scalar Field Plane wave solutions of the Klein Gordon equation. Internal symmetries and Noether's theorem.

Free QFT. (5 lectures) Quantisation and commutation relations. Creation and annihilation operators. Time and QFT. Complex scalar fields and their conserved charge.

Interacting QFT. (14 lectures) Interaction Picture and S matrix. Wick's theorem and normal ordering. Simple Feynman diagrams in coordinate and momentum spaces. Cross sections, matrix elements and vacuum expectation values. Vacuum diagrams. Basic example of mass renormalisation.

Note that Fermions were included by previous lecturers so you will find some older exam papers contain questions no longer covered by this course though the Unification course will look at classical fermions and QFFF MSc will cover fermions in QFT in other courses. 

Office Hours

Exam Office Hour, from now until the exam on Wednesday 22nd May.

  • Tuesday 11am
  • Friday 10am

Rapid Feedback Classes

The first QFT Rapid Feedback Class for Autumn 2018 is in week 2 on Thursday 11th October at 1pm in Lecture Theatre 2 (again check your timetable).  Later ones are then on alternate weeks (so all even weeks) on Fridays at 17.00 in Lecture Theatre 2 but check your timetable for the lastest information. 

The rapid feedback sessions are run by a PhD student Lucas Wallis from the theoretical physics group. For each rapid feedback class the lecturer will nominate a couple of questions from one of the problem sheets. If students wish written feedback on their answers to these nominated questions only, they hand their work on those two questions to the Physics Undergraduate Student Administrative Office on Level 3 in Blackett by 12.00 on Monday 8th October for the first session and then 12.00 on Wednesday before every other presentation.  The UG office on level 3 Blackett will provide boxes for this. The PhD student will provide written feedback on answers (for the nominated questions only) and will return these scripts, either at his presentation on the following Friday or via the student office again.

Handing in the work and/or attending the rapid feedback classes are optional. This work does not contribute to the course assessment. Students are strongly advised to make use of this opportunity for feedback and extra tuition.

Note that only the nominated questions are dealt with by the PhD student in charge of rapid feedback.  I provide full answers for all questions and am happy to discuss the problem sheets in my office hours.

Rapid Feedback Timetable Autumn 2018

Please refer to the official timetable which is the definitive guide.  To gain written feedback, hand in your work to the Physics Undergraduate Student Administrative Office on Level 3 by noon on the Tuesday before the presentation unless stated below.

  • Week 2: Thursday 11th October, PS1, Q2 and 4. Note hand in for feedback for this rapid feedback only is by noon on Monday 8th October to UG office.
  • Week 4: Friday 26th October, PS2, Q3 and 4.
  • Week 6: Friday 9th November, PS4, Q1 and 4.
  • Week 8: Friday 23rd November, PS5, Q2 and 3.
  • Week 10: Friday 7th December, PS6, Q3 and 4.

Problem Sheets, Handouts, Notes

Syllabus for the Autumn 2018 QFT course which has not changed from last year.

David Tong's QFT lecture notes match this course well.

Tim Evans' handwritten QFT notes .  I will try to keep these updated but changes are now relatively small from year to year. 

QFT Lecture Notes 2017 taken by Stav Zalel (PhD student note taker so should be very similar, if much neater, version of lecturer's notes)

Individual handouts (also see below for supplementary material not handed out):- 

Problem Sheets and Solutions

Problem Sheets: 

  • PS1 (11/10/17) Annihilation and Creation Operators.
    Students must be able to handle this problem sheet before taking this course. I will assume students are already experienced in handling such operators and I will not be covering this aspect in the course. See my course summary handout for more details.
  • PS2 (8/10/18) One-Dimensional Model (ring of masses)
  • PS3 (8/10/18) Classical Field Theory. 
  • PS4 (5/11/18) Free Scalar Quantum Field Theory
  • PS5 (22/10/18) Generic Interacting Quantum Field Theory
  • PS6 (20/11/17) Feynman Diagrams in Coordinate Space
  • PS7 (4/1/19) Interacting Quantum Field Theory: λφ4 

Solutions are posted about a week after Problem Sheet material has been covered in lectures or just after the hand in has been made for any relevant Rapid Feedback: 

PS1 Answers 11/10/17,‌ PS2 Answers (8/10/18), PS3 Answers (8/10/18)PS4 answers (22/10/18), PS5 Answers (1/5/19), PS6 Answers (3/1/19)PS7 Answers (4/1/19) 

Supplementary Material

This may be of interest or use to supplement other material.  

  • Note the videos on Panopto (links elsewhere on this website). 
  • These notes on Classical Field Theory‌ are taken from a longer set of notes I made for my old Unification course.
    Those doing the Unification course might find my old incomplete notes on 
    Symmetry and Unification useful. They contain a brief overview of the background particle physics and group theory needed for Unification so may be of use more generally. The notes are unfinished in places so use with care.‌ I have no plans at the moment to finish these Unification notes but will happily make small corrections if they are pointed out to me.
  • Haisch's notes on Wick's theorem‌, taken from Interacting Fields notes‌.
  • Chapters 1 and 2 of the lecture notes on QFT by Timo Weigand look useful.  Some material in those is not in this course but will be useful for QFFF students, as will the later chapters.

Past Exams

QFT examination

This is a final exam which is the same for undergraduates and postgraduates. The assessment for this course is based only on this exam. 

The Syllabus for the Autumn 2018 QFT course lists the examinable material. All material covered in the lectures is examinable except for the lecture on Fermions.  Material in the problem sheets is examinable except for those questions marked as optional. The questions marked with a star in the problem sheets are core material, those unmarked are important, but I will not assume any knowledge of questions marked optional. I could draw on material contained in the optional questions but this would only to be for the last few marks of a paper and I will not assume any prior knowledge.

The current course will be reflected in exams from May 2015 onwards. Earlier exams will contain some material no longer in the syllabus. However, the structure of the 2015 exam will be the same as recent years. That is students will have to answer three out of four questions, each question marked out of 30. Note that the department's policy is to put out solutions for undergraduate exams only every three years. However much of the material is derived from the problem sheets so you should find most answers in their solutions.

A Blank QFT Exam is available to illustrate the current format.  Note in particular that a new appendix of formulae has been added for use in the exam in 2018 but this may be updated every year.

Previous less relevant exams are 2006, 2007, 2008, 2009, 2010, 2011 and 2012. Solutions for undergraduate exams for the 2009 and 2012 are provided here, reproducing what is on the department's examination answers web page (Department of Physics - Students - Current Students - Undergraduates - Examinations).

New Year test

The QFFF MSc students only have the option to take a test on the QFT course early in the New Year (typically one of the first few days of Spring term). Students on other courses cannot take this test, but the material may be of use for revision purposes. This test is taken in exam conditions but the marks are only used to provide feedback to QFFF students. The test does not contribute to the final mark for the course. The New Year test is also used to support QFFF students by providing staff with useful information when writing references as many QFFF students have only been here for only a few months (though this is not a service provided by most MSc courses). The test will be made available here as soon as the formal test has finished as the test material may be of use to anyone revising for the final exam.

The test is not a mock exam and it is not necessarily in the style of the final exam but the test is likely to share several features with the final exam. In particular, it covers exactly the same material as detailed for the exam. The January 2019 test was three questions with no choice while the final exam requires three questions out of four. Both are two hour exams. The questions in the tests are in the style of those I set in the summer QFT exams so past summer exams serve as a good guide for this test and vice-versa.

Like the final exam, only tests from 2015 onwards will reflect the current syllabus exactly, previous tests may contain material no longer on the syllabus but are provided below in case they are of use.

2006 Test2007 Test2008 Test2009 Test2010 test2011 test2012 test, ‌

2012 Test Solutions2014 Test Solutions

Videos of Lectures

The primary source is the Imperial College Panopto site which is the definitive and most up to date source - search for "Quantum Field Theory".

I adjust the settings for each video by hand (hopefully soon after the lecture but sometimes there may be a delay of a day or two) to maximise availability within College but I am limited by College policy in what I can do. The access lists are maintained by hand so may not be always up to date so if you have a problem contact me and I will pass your name on. In some cases sound may be poor - do remind me to wear the microphone and to make sure they are not muted. In some rare cases, the lecture may not have been recorded for some technical reason. Feedback on these videos (were they useful, how did you use them, ideas for improvements) welcome.

This list of links below is updated by hand often a few days after lectures so try the main Panopto site for latest videos. 

Autumn 2018 Course

Autumn 2017 Course


Autumn 2016 Course

Autumn 2015 Course

Another list of the Autumn QFT 2015 Course Videos is available. Just ignore the fermion lecture for 2016 onwards.

Some of the Autumn QFT 2014 Course Videos are available too.

Handwritten Notes

Handwritten Notes 2017

These are a photcopy of my own notes and are not intended for student use.  They may not reflect what was actually said as I may improvise in a lecture.  I provide my notes as is in case they are any use. The notes have been corrected over the last few years so most errors have been eliminated from the older notes. At the same time, I do rewrite sections every year so new errors creep in.  Do flag up any queries with me, I'm happy to correct mistakes or explain issues but I would rely on David Tong's typed notes for factors of i or signs.

Another much neater version of my notes are the QFT Lecture Notes 2017 taken by Stav Zalel, a PhD student note taker.  They are based on what she heard in my lectures and has generously provided them for all student.  Again, please note they are again provided as is. Every lecture should be here in this single pdf version, contact Tim Evans if a lecture is missing.

A list of Tim Evans' handwritten QFT notes or try links below (lecture notes‌ also online)