There’s another new article in the physics for mathematicians series. This one picks up the story of quantum field theory right where the previous one left off. It explores how we can take the ideas we’ve developed so far and turn them into an algorithm for computing scattering amplitudes. In particular, this article finally introduces the famous Feynman diagrams and explains where they come from and how they fit into the story we’ve been telling across this series of articles.
In order to make this article flow better, I had to do something I don’t ordinarily like doing and make a small notational change to the previous article in the series. (In the older version, I didn’t distinct between the vacuum state of a free theory and the vacuum state of an interacting theory, and wrote for both. In the newer version, the free vacuum is called and the interacting vacuum is called .) That change is now live as well. My hope is that, if you’ve been following this series so far this isn’t too big a disruption, and I’ll try not to change the past out from under you again if I can help it!
My current plan for the quantum field theory series is that there will be one more article (on the topic of renormalization) in the “main” series, but that I might end up writing a few one-offs on some smaller topics in quantum field theory to go along with them. If this plan ends up being what happens, the picture is that the first four articles will serve as the trunk of the tree, and that the others will branch off from it and could potentially be read in any order.
It’s been very fun for me to finally arrive at the point in my study of this subject that I feel competent to put together these expositions! Quantum field theory is something I’ve been working toward mastering for a very long time now, and I’m happy to finally get the chance to share what I’ve managed to learn with others to whatever extent these articles can do that. As I always say, do let me know if there’s any topic you’d like to see covered in this style, whether it’s physics-related or not, and I’d always love to hear from any readers if you have comments, questions, corrections, or anything else you’d like to talk about.