*An online video sketch “Why Learn QFT?” is available at MacVideo (here), so you can taste this course’s ideas and try on the online lecture format. Links to recordings of the lectures given when this course was taught during Covid are also available at this same MacVideo channel.*

This course aims to provide an introduction to quantum field theory for undergraduates. Quantum field theory is normally not taught until graduate school, which is a shame because it is the language used at the frontier in almost every discipline of modern physics. Yet there is no fundamental reason why it could not be taught at the undergraduate level, apart from the obvious observation that an undergraduate physics curriculum is already pretty full.

Students are assumed to have had a first exposure to special relativity and to non-relativistic quantum mechanics and electromagnetism at a level common at 3rd or 4th year in an undergraduate program. (Some knowledge of statistical physics is also useful, but not required.)

In essence, quantum field theory is the formulation of quantum mechanics that allows one to describe processes that can change the number of particles involved. Because it turns out to very efficiently bake in a few core properties shared by all known physical laws, quantum field theory is also widely used even for systems whose total number of particles never changes.

As the course will show, once relativity and quantum mechanics are combined it is a basic fact that *all* interactions necessarily change the number of particles. (This is related to the reason why antiparticles must exist.) For this reason quantum field theory seems to be the language in terms of which Nature’s fundamental laws are necessarily written. But QFT does not require relativity and this course first introduces the tools of QFT before then introducing the additional baggage required for relativistic QFT.

Although I work from my own notes (that are a work in progress, available here) sometimes it is useful to have alternative points of view. Two qualitative approaches to the subject that might be useful (but are not required) are “Quantum Field Theory for the Gifted Amateur” by Blundell and Lancaster, or “Quantum Field Theory in a Nutshell” by Zee, or “A Prelude to Quantum Field Theory” by Donoghue and Sorbo. See below for procedural course information. The table of contents of the notes provides the most detailed syllabus, but is paraphrased here.

#### SYLLABUS

**Multiparticle Quantum Mechanics**- Bosons
- Fermions
- Quantum Statistical Mechanics

**Creation and Annihilation Operators**- Heisenberg’s Treatment of the Harmonic Oscillator
- Creation and Annihilation Operators
- Fermions and Anticommutation Relations
- Completeness of Operators

**Interactions**- Perturbation Theory
- Emission and Absorption
- Stimulated Emission
- Pauli Blocking and 2-body Scattering
- Equilibrium and Detailed Balance
- Coherent States
- Bosons and Macroscopic Forces

**Fields**- Locality and Cluster Decomposition
- The Schrodinger Field and Second Quantization
- Bose-Einstein Condensation
- Spontaneous Symmetry Breaking

**Relativistic Quantum Mechanics**- The Electromagnetic Field
- Relativity of Simultaneity and Antiparticles
- Crossing Symmetry, CPT Invariance
- Spin-Statistics Connection

**Quantum Electrodynamics**- The Dirac Field
- Gauge Invariance
- Relativistic Feynman Rules

#### COURSE INFORMATION

The procedural information relevant to this course is given below.

#### Lectures

Classes are in person in the Winter 2023 term and will be held in HH104 from 1:30 – 2:20 on Monday, Wednesday and Thursday of each week of the term. Classes were online and recorded during the pandemic and these recordings are available at MacVideo (here), including a “Why Learn QFT?” preliminary, so you can try it on before enrolling.

For best results the class should pre-read sections of the lecture notes and/or pre-view some of the online lectures.

Attendance to the lectures is certainly not compulsory, but if you come I do ask you to pay attention and not disrupt the class with personal conversation or social media. I will do what I can to ensure that you do not have to gnaw your own arm off to stay awake.

#### Textbook

There is no official course textbook; I provide notes which lay out the course much as I will present it in the lectures. The goal of these notes is to provide more detail and to provide a written record to allow you to focus on what is being said in the lectures. (I do recommend making your own notes as well, though, since writing your understanding helps absorb the material more robustly. A current version of my notes (that I continually update as the term progresses) can be found here.

For those seeking alternative viewpoints, David Tong also has a good set of lecture notes (though at a graduate level) at his Cambridge University webpage.

#### Office Hours

Because I spend half my time at Perimeter Institute I may be hard to find in my office. So it is worth setting up any appointments in advance, and the best way to do so is to contact me by email at cburges – at – mcmaster.ca (notice the single “s” – sigh). I will also linger immediately after the scheduled lecture times since we are already together then. Otherwise, feel free to arrange another time with me on an individual basis. (I will make a point of being there for scheduled appointments, so if you *do* set up an appointment, please show up or give me adequate warning that you cannot make it!)

#### TA

Sara Bogojevic will be our course TA whose email coordinates are sbogojevic (at) perimeterinstitute.ca. A schedule for online office hours will be posted here, but feel free also to make appointments separately.

#### Assignments

The course work involves completing a (roughly) weekly assignment. Like any worthwhile subject, Quantum Field Theory is a contact sport and so is only really learned by doing. It is very very strongly recommended to work the assignments even if you only audit the course.

I will be issuing assignments during class on Fridays (as mutually agreed at the second lecture), and they are due in class the following week.

The first assignment (due Friday Jan 27) is here, with solutions here.

The second assignment (due Friday Feb 3) is here, with solutions here.

The third assignment (due Friday Feb 10) is here, with solutions here.

The fourth assignment (due Friday Feb 17) is here, with solutions here.

The fifth assignment (due Friday Mar 10) is here, with solutions here.

The sixth assignment (due Friday Mar 31) is here, with solutions here.

The seventh assignment (due Friday Apr 7) is here, with solutions here.

Solutions to the Midterm are here.

**Important message from Sara:**

- From now on, please submit your assignment solutions as
**a single pdf file**to the following Dropbox link https://www.dropbox.com/request/aEfVbWnzFndRJVJN1aaG . Dropbox will prompt you to type in your**full name**and**email address**as well – please don’t skip this step since you’ll then get a confirmation of which file you submitted and I’ll know who sent which file. - Starting from assignment 2 there will be a
**penalty of -10%**of the total points for late submissions that are sent in by the end of Sunday. Any assignments that are submitted after the Sunday following the original deadline will receive 0 points.

There will not be assignments in the week of Feb. 27 to Mar 3 due to the midterm.

You are welcome to work together on figuring out the assignments, though everyone must write up and submit their own solutions. It should go without saying, while you are allowed (for assignments) to consult internet material about conceptual information, you are never permitted to plagiarize material from the internet (or to use internet cheating tools like chegg) when preparing any work for marks, including assignments.

#### Term Project

The term project is to summarize in your own words one of the classic papers of quantum field theory. Describe both what the paper’s intended point was, and why it was important (these are not always the same thing). You can work in groups if you wish, but if so when you submit your paper choice you should also submit a list of the others in your group.

Procedural details and a lengthy list of papers from which to choose can be found here.

Step one: choose a paper from the list (or you can choose one not on the list if you first get my approval for the paper you have in mind) and tell the TA which it is (and who your fellow group members are, if any) by Thursday February 16, 2023.

Step two: hand in your finished essay in class by Thursday April 6, 2023.

When preparing this essay you are allowed to consult internet sources for conceptual and historical information, provided that you cite this properly in the essay. You are never permitted to plagiarize material from the internet when preparing any marked work, including essays.

#### Midterm Exam

Since the course is online, the midterm test will be held in class on Thursday March 2nd, 2023.

The midterm provides the best possible practice for the final exam, so it would be silly not to write it. Those who do not write the midterm for whatever reason can avail themselves of marking Option B below.

Perhaps needless to say, you are never permitted to plagiarize material from the internet when performing a midterm exam.

#### Final Exam

The Final Exam will be held during the April examination session.

You are never permitted to plagiarize material from the internet when preparing any marked work, and this is especially true for final exams.

#### Marking Scheme

The course marks are completely based on the weekly assignments, the mini-quizzes, the midterm test, the term project and the final exam. The term mark will be computed from these according to whichever of the following formulae maximizes your final mark:

- A) Ass.: 20% Midterm: 20% Term Project: 20% Final Exam: 40%
- B) Ass.: 20% Midterm: 0% Term Project: 20% Final Exam: 60%
- C) Ass.: 20% Midterm: 20% Term Project: 10% Final Exam: 50%
- D) Ass.: 20% Midterm: 0% Term Project: 10% Final Exam: 70%

You do ** not** have to choose in advance which one you want; I will compute all four and give you the maximum.

Part of the reason for providing you this menu of alternatives is to allow you to accommodate the imponderables of your own life, such as unexpected illnesses and the like. The purpose of doing so is to make this flexibility open to *everybody* in the class, and not just to those who wish to make special arrangements with me, or with the Associate Dean. In particular, this my preferred way to deal with MSAF applications in this class.

#### Additional Work and Supplemental Exam:

Additional work will NOT be available for students who might wish to improve their marks. The standard McMaster rules apply regarding the availability of supplemental exams.

#### Reading you your rights:

The Centre for Student Development offers free academic skill support.

Although hopefully it does not need saying, be warned that the University does not tolerate cheating, plagiarism and the like:

THE UNIVERSITY VALUES ACADEMIC INTEGRITY. THEREFORE ALL STUDENTS MUST UNDERSTAND THE MEANING AND CONSEQUENCES OF CHEATING, PLAGIARISM AND OTHER ACADEMIC OFFENCES UNDER THE CODE OF STUDENT CONDUCT AND DISCIPLINARY PROCEDURES

(see http://www.mcmaster.ca/academicintegrity for more information).