This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

### Courses

### Fall 2022 Courses

Usual Meeting Time: Tuesdays from 10am-Noon and 230pm-430pm.

### Winter 2022 Courses

Usual Meeting Time: Mondays and Thursdays from 4:00 pm - 5:20 pm

### Fall 2020 Courses

Usual Meeting Time: Tuesdays and Thursdays from 3:30 - 5:00 pm

This course provides a graduate-level introduction to computational fluid dynamics, covering the theoretical concepts and numerical methods that form the foundation of much of modern theoretical astrophysics and cosmology. Beyond applications in astrophysics and cosmology the concepts introduced here are of relevance in many other fields of physics and engineering. Assignments will include both analytical problems and hands-on programming problems. The latter will be python-based and are designed to provide a deeper understanding of the numerical concepts through practical implementation. A brief introduction to python and jupyter notebooks will be given.

### Spring 2020 Courses

This course has two main goals: (1) to introduce some key models from condensed matter physics; and (2) to introduce some numerical approaches to studying these (and other) models. As a precursor to these objectives, we will carefully understand many-body states and operators from the perspective of condensed matter theory. (However, I will cover only spin models. We will not discuss or use second quantization.)

Once this background is established, we will study the method of exact diagonalization and write simple python programs to find ground states, correlation functions, energy gaps, and other properties of the transverse-field Ising model. We will also discuss the computational limitations of exact diagonalization. Finally, I will introduce the concept of matrix product states, and we will see that these can be used to study ground state properties for much larger systems than can be studied with exact diagonalization.

Each 90-minute session will include substantial programming exercises in addition to lecture. Prior programming experience is not expected or required, but I would like everyone to have python (version 3) installed on their computer prior to the first class, including Jupyter notebooks; see “Resources” below.

The goal of this course is to introduce the path integral formulation of quantum mechanics and a few of its applications. We will begin by motivating the path integral formulation and explaining its connections to other formulations of quantum mechanics and its relation to classical mechanics. We will then explore some applications of path integrals. Each 90-minute session will include roughly equal amounts of lecture time and activities. The activities are designed to enhance your learning experience and allow you to assess your own level of understanding.

The aim of this course is to understand the thermodynamics of quantum systems and in the process to learn some fundamental tools in Quantum Information. We will focus on the topics of foundations of quantum statistical mechanics, resource theories, entanglement, fluctuation theorems, and quantum machines.

The aim of this course is to explore some of the many ways in which symmetries play a role in physics. We’ll start with an overview of the concept of symmetries and their description in the language of group theory. We will then discuss continuous symmetries and infinitesimal symmetries, their fundamental role in Noether’s theorem, and their formalisation in terms of Lie groups and Lie algebras. In the last part of the course we will focus on symmetries in quantum theory and introduce representations of (Lie) groups and Lie algebras.

### Winter 2020 Courses

### Fall 2019 Courses

Usual Meeting Time: 10:00-12:00

### Spring 2019 Courses

### Fall 2018 Courses

Usual Meeting Time: Every Wednesday from 10:30am to 12:00pm

### Winter 2018 Courses

### Fall 2017 Courses

Usual Meeting Time: 4-5:15

### Spring 2017 Courses

### Winter 2017 Courses

### Fall 2016 Courses

Usual Meeting Time: Wednesdays, 2-3:30