A few years ago, before finishing graduate school, I embarked on a quest to understand quantum field theory and the standard model of particle physics. My first project for this blog is going to be about the physics I learned along the way. My training is as a mathematician, and these articles are written with an audience in mind that’s a lot like me when I first started trying to learn this stuff. In particular, this means that I’m going to be assuming familiarity with some mathematical machinery that isn’t always part of the standard presentation of these ideas.

The point of this isn’t to exclude people (although sadly it probably will) but because I’m trying to fill a gap that I saw when I was trying to absorb this material from physics books. A lot of explanations of the “mathier” parts of physics are, despite their mathiness, written with a audience of physicists in mind, and so naturally emphasize the aspects of the situation which are relevant to solving physical problems. If your goal is to solve physical problems — as it should be for most of the people who learn physics — then this is the right thing to do. But for the reader who understands the mathematical machinery from a more general context, reading these sorts of explanations can be a bit of a slog, and it can often be unclear which parts of the text are “just math” and which parts are “doing physics.” My aim is to present these ideas in a way that makes that distinction clear.

Despite this, though, I’m also going to try to avoid falling into what I see as the opposite trap: using the physics merely as an excuse to justify talking about interesting math. I of course very much enjoy talking about interesting math, and I hope to do it elsewhere on this blog, but the end goal of the presentation in this series is to understand the physics.

The articles in this series so far are:

- Hamiltonian and Lagrangian Mechanics
- Quantum Mechanics I - Foundations
- Connections Crash Course. This article comes with two short supplements, on G-Bundles and Holonomy and Curvature.
- Electromagnetism as a Gauge Theory