I’ve just finished a supplement to the general relativity article I posted a few weeks ago in the physics for mathematicians series. This one is about the Lagrangian approach to general relativity; while it’s a bit more abstract than the approach I took in the main article, I found when learning the theory that it offered a very useful perspective, so I wanted to share it. The article also contains an exploration of a topic that I got quite stuck on when learning this material myself: the relationship between the energy-momentum tensor as it emerges from Einstein’s theory and the concept of energy-momentum we already have from non-gravitational physics.
I’m still working on other articles for this series. The next one might be the one on Lagrangians in classical field theory I mentioned in the last update, and it might also be the third entry in the quantum field theory sequence, which I currently expect will end up being around four to six articles long. As always, if there’s a topic you’d like to see covered in this style, please reach out and let me know!
After almost a year I’ve finally finished another new article in the physics for mathematicians series. This one is a quick introduction to general relativity, especially aimed at people who are already at least a little familiar with concepts like connections and curvature in the context of Riemannian geometry. This one was very fun for me to write, so I hope that if you’re interested in the topic you enjoy it too!
I do intend to keep working on this series, although probably still at this very slow pace. I’m currently thinking that the next one will be an overview of how to use Lagrangians in classical field theory. As always, though, if there’s a topic you’d be interested to see covered in this style, feel free to reach out and let me know.
I visited Mathcamp for just one week this summer, and I’ve just posted notes for the class I taught there. If you’re one of the students who was in that class and you happen to be reading this, thanks again for a wonderful week!
I’ve just posted another new article in the physics for mathematicians series. This one introduces interacting quantum field theories, including a discussion of how to talk about particles in an interacting theory, moving from there to a discussion of particle scattering and a result called the LSZ formula, which we’ll use in the subsequent installment to do computations with the famous Feynman diagrams.
More than any other topic I’ve covered in this series, I am very aware that this one is reaching an even smaller audience than usual. It’s a topic I care a lot about, and I’m going to keep working on it for that reason, but I think for the next physics article I’d like to aim for a topic with a bit more reach. (By the way, if you’re enjoying the QFT articles and I haven’t heard from you, you should reach out!) Right now I’m thinking that that means general relativity, which has the advantage of not requiring a lot of physics background to appreciate, but I am of course open to suggestions.
I’ve posted a new article, this time outside the physics series. As the name suggests, it’s an overview of the relationship between the Riemann zeta function and the distribution of the primes, and my hope is that it’s readable to anyone who knows enough complex analysis to have seen the Residue Theorem but who might not know anything at all about analytic number theory. This article grew out of a series of lessons I put together for one of my tutoring students, and I really enjoyed learning the material well enough to write it. (By the way, I also currently have some openings for new students! Reach out by email if you’re interested.)
I am also finishing the final edits on a second quantum field theory post, which should be up pretty soon.