## Quantum Field Theory I: 721

### Notices

**Week 9:** Office hours are at **1-2 pm** on Tuesday, via Zoom, and our Thursday class is at **1-2 pm via Zoom**.

**Week 8:** There is an extra class at 8:30 am on Friday October 16 in Small 122.

**Week 2:** There is no Zoom session on Thursday September 3.

Look after yourself and those around you! This is a very stressful and difficult time for everyone, so please be compassionate with yourself and those around you, and look after yourself. Don't forget that Social Distancing doesn't have to mean Social Isolation! There are lot of good mental health resources available online, such as virusanxiety.com.

##### What hybrid mode means for us in practice:

- Mini-lectures will continue to be pre-recorded and posted here.
- Tuesday 11:00 am to 12:20 pm will continue to be office hours via Zoom.
- Thursdays 11:00 am to 12:20 pm will take place in Small 122.

### Course basics

Let's start by acknowledging that this is going to be a very strange, and difficult semester. It is highly likely that the course will have to evolve as the semester progresses, and we'll have to try to adapt as best we can. We will have to work together with patience and understanding, because we will all be going through this for the first time together, but we will get through it! Please let me know if there is anything I can do to help you navigate the course, and the semester more generally.

We will work in a blended (or hybrid) mode: you will cover much of the material remotely, through short lectures and readings, and we will focus on problem solving, conceptual questions, and more difficult topics during our weekly in-person class time. Each week, you will watch a few mini lectures, generally around ten to fifteen minutes each, and work through readings. The mini-lectures will highlight key concepts and introduce to the readings, which provide mathematical details. The readings will largely be taken from Peskin and Schroeder's textbook, Quantum Field Theory (the student edition is available online through the library here [log-in required]), and David Tong's lecture notes [here]. My (hand written) notes will be available on this webpage to supplement the readings.

### Course details

**Class schedule:** Our in-person class time will take place in Small Hall 122 on **Thursday 11:00-12:20**. Mini lectures and readings will be uploaded to the course webpage on Monday mornings (usually by 11:00 am).

**Textbook:** The best textbook for this course is Peskin and Shroeder's *An Introduction to Quantum Field Theory*. (The student edition is available online through the library here [log-in required]). We will also be using David Tong's QFT lecture notes and Schwartz's textbook *Quantum Field Theory and the Standard Model* for some of our readings. See the syllabus for a brief discussion of other textbooks and useful resources. There is a more extensive literature review by Flip Tanedo here [external link].

**Prerequisites:** *Physics 622*. Knowledge of quantum mechanics and special relativity.

**Instructor:** Chris Monahan (he/his/him), Small Hall 326C [not that it matters this semester]. Email: cjmonahan'at'wm.edu.

**Course grading:** Assessment will consist of weekly problem sets (60%) and a take-home final exam (40%). The class has voted! The final exam will be a take-home project, submitted in the style of a peer-reviewed article, written in LaTeX. Two of the problem sets will be replaced by a mini-project in the middle of the semester, to help familiarise everyone with the format and with using LaTeX.

**Problem sets** Problem sets will be posted here on Wednesday mornings and are due the **following Wednesday at 5 pm (17:00)**. All problem sets should be **submitted by email**. The first problem set will be posted Wednesday August 26 and will be due Wednesday September 2. I will drop the lowest grade on your weekly problem sets (excluding the mini-project).-->

**Office hours:**By Zoom on Tuesdays 11-12:20.

### Course description

What is the Universe really made of? Are there new fundamental particles we haven't found yet? Just how cool is the Large Hadron Collider (LHC)?

Quantum field theory is the mathematical framework that underpins our attempts to answer these questions. Except for the third, for which the answer is obviously: very. Grappling with quantum field theory is key to understanding particle and nuclear physics, and much of condensed matter physics.

We will cover:

- Classical field theory.
- Free scalar fields.
- Interacting scalar fields.
- The Dirac equation.
- Quantising the Dirac field.
- Quantum electrodynamics.

### Syllabus

The syllabus can be found here (pdf).### Course materials

### Week 0

**Notes:**week 0.**[Background] reading:**Wilczek: Quantum field theory.

### Week 1

**Minilecture videos:**video 1, video 2, and video 3.**Notes:**week 1.**Readings:**Tong Section 0; P&S Sections 2.2 and 2.3; Schwarz Sections 3.1, 3.2, and 3.3.**Quick quiz:**week 1.**Example problem:**week 1.

### Week 2

**Minilecture videos:**video 1, video 2, and video 3.**Notes:**week 2.**Readings:**Tong Sections 2.4, 2.6, and 2.7; P&S Section 2.4; Schwarz Section 6.2.**Extra readings:**Tong Section 2.3.

### Week 3

**Minilecture videos:**video 1 and video 2.**Notes:**week 3.**Readings:**Tong Sections 3 (introductory part) and 3.1; P&S Section 4.1 and 4.2.**Quick quizzes:**week 2 and week 3.**Example problem:**week 3.

### Week 4

**Minilecture videos:**video 1 and video 2.**Notes:**week 4.**Readings:**Tong Sections 3.3 and 3.4; P&S Sections 4.3 and 4.4; Schwarz Sections 7.1, 7.2, and 7A (appendix).**Quick quizzes:**week 4.**Example problem:**week 4.

### Week 5

**Minilecture videos:**video 1 and video 2.**Notes:**week 5.**Summaries:**scalar field summary and scalar field flowchart.**Readings:**Schwarz Sections 5 (intro), 5.1, 6 (intro), and 6.1; Tong Sections 3.2, 3.3.3, 3.5, and 3.6.**Quick quizzes:**week 5.**Thursday notes:**week 5.

### Week 6

**Minilecture videos:**video 1, video 2, and video 3.**Notes:**week 6.**Readings:**Schwarz Sections 10.1, 10.2, and 10.3; Tong Sections 4.0, 4.1, 4.2, and 4.3; P&S Sections 3.1, 3.2, 3.3, and 3.4.**Quick quizzes:**week 6.

### Week 7

**Minilecture videos:**video 1, video 2, and video 3.**Notes:**week 7.**Readings:**Tong Sections 4.4, 4.6, 4.7, and 5.2; P&S Sections 3.5 and 3.6; Schwarz Sections 11.2, 11.4, 11.5, 11.6, and 12.3.**Extra readings:**Tong Section 4.5 and 5.1; Schwartz Sections 10.5, 10.6, and 11.3.**Quick quizzes:**week 7.

### Week 8

**Minilecture videos:**video 1, video 2, and video 3 [TVBC].**Notes:**week 8.**Readings:**Tong Sections 5.4, 5.5, 6.1, and 6.2; P&S Section 4.7; Schwarz Sections 8.23, 8.3, 8.42, and 8.5.**Extra readings:**Schwartz Sections 8.4 and 8.6.**Quick quizzes:**week 8.**Thursday notes:**week 8.

### Week 9

**Minilecture videos:**video 1 and video 2.**Notes:**week 9.**Readings:**Tong Sections 6.3, 6.4, and 6.5; Schwarz Sections 10.4, 13.0, 13.1, 13.2, and 13.3; P&S Section 5.1.

### Problem sets

The links below should take you to PDF copies of the problem sets for each week. Each problem set is graded out of twenty points. Problem sets are due at 17:00 the following Wednesday. Please submit your problem set solutions as PDF files, via email, and remember to include your name in the filename, which makes my life a lot easier.- Problem Set 1, 08/26/20 and solutions.
- Problem Set 2, 09/2/20 and solutions.
- Problem Set 3, 09/9/20 and solutions.
- Problem Set 4, 09/16/20 and solutions.
- Problem Set 5, 09/23/20 and grading rubric and one possible solution.
- No problem set in week 6.
- Problem Set 6, 10/7/20 [
**optional**] and solutions. - Problem Set 7, 10/14/20.
- Problem Set 8, 10/21/20.