## Quantum Field Theory I: PHYS 721 [Fall 2021]

### Notices

All problem sets are due on **Tuesday December 7**.

### Course basics

Let's start by acknowledging that this could end up another strange and difficult semester. It is quite possible 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 an in-person mode, with two in-person classes each week. Much of the material is based on Schwartz's textbook *Quantum Field Theory and the Standard Model*, although you will also find 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 235 on **Tuesdays** and **Thursdays 11:00-12:20**.

**Textbook:** The best textbook for this course is Schwartz's textbook *Quantum Field Theory and the Standard Model*. We will also be using David Tong's QFT lecture notes and Peskin and Shroeder's *An Introduction to Quantum Field Theory* (The student edition is available online through the library here [log-in required]). 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. 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 Thursday mornings and are due at the **start** of the **following Thursday class**. All problem sets should be **submitted by email**. The first problem set will be posted Thursday September 9 and will be due Thursday September 16. I will drop the lowest grade on your weekly problem sets.

**Office hours:**Small 326C on Tuesdays 3-4 pm.

### 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:

- Review of relativity and classical field theory.
- Representations of the Lorentz group, including spin 0, spin 1/2, and spin 1.
- Gauge symmetries and electromagnetism.
- Quantisation of scalar, spinor and gauge fields.
- First infinities and normal ordering.
- Scattering cross-sections and decay rates.
- S-matrix, time ordering, and the LSZ reduction.
- Spin and statistics.
- Propagators, Green functions, and Feynman rules.
- Scalar quantum electrodynamics.
- Quantum electrodynamics.
- Sample scattering processes in quantum electrodynamics.

### Syllabus

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

### Week 0

**Notes:**Thursday.**Quick quiz:**Quick quiz 0.**[Background] reading:**Wilczek: Quantum field theory.

### Week 1

**Notes:**Tuesday and Thursday.- Problem Set 1, 09/09/21 [Due on
**Tuesday September 21**] and solutions.

### Week 2

**Notes:**Tuesday.**Quick quiz:**Quick quiz 1.

### Week 3

**Notes:**Tuesday and Thursday.**Quick quiz:**Quick quiz 2.- Problem Set 2, 09/23/21 and solutions.

### Week 4

**Notes:**Tuesday and Thursday.**Quick quiz:**Quick quiz 3.- Problem Set 3, 09/30/21 and solutions.

### Week 5

**Notes:**Tuesday and Thursday.**Quick quiz:**Quick quiz 4.- Problem Set 4, 10/07/21 and solutions.

### Week 6

### Week 7

**Notes:**Thursday.- Problem Set 5, 10/21/21 and solutions.

### Week 8

**Notes:**Tuesday and Thursday.**Quick quiz:**Quick quiz 5.- Problem Set 6, 10/28/21 and solutions.

### Week 9

**Notes:**Tuesday and Thursday.- Problem Set 7, 11/4/21 and solutions.

### Week 10

**Notes:**Tuesday and Thursday.- Problem Set 8, 11/4/21 [Due on
**Tuesday November 23**] and solutions.

### Week 11

**Notes:**Tuesday and Thursday.**Quick quiz:**Quick quiz.

### Week 12

**Notes:**Tuesday.

### Week 13

**Notes:**Tuesday, Thursday, and polarised scattering examples.- Problem Set 9, 11/30/21 [Due on
**Tuesday December 7**] and solutions.

### Week 14

**Notes:**Tuesday and Thursday.**Quick quizzes:**Quick quiz 7 and Quick quiz 8.

### Exam

The link below should take you to a PDF copy of the exam, due on**Tuesday December 21**at

**5 pm**. The exam is graded out of sixty points.