Just under the wire to get it out in 2020, I’ve posted another new article in the physics for mathematicians series about Feynman’s path integral formulation of quantum mechanics. As always, just because one of these pieces has gone up that doesn’t mean I’m not still interested in making improvements, so let me know if you have any to suggest!
While it is going quite slowly, my intention for this series is still to slowly build toward the exposition of quantum field theory I wish I’d read many years ago, and this piece is one of the bricks in that wall. I’m a bit unsure of where I’ll go next. The last thing I think I’d really like to cover before diving into QFT proper is a discussion of how renormalization arises in statistical mechanics, but there are also a few topics — like general relativity for example — that are still very interesting despite not being part of this particular narrative thread. Feel free to reach out if there’s a topic (even one I haven’t listed, or even something that isn’t physics) that you’d like to see covered in this style.
I’ve posted a new article in the physics for mathematicians series, the promised piece on thermodynamics and statistical mechanics. This one ended up being quite long, but I learned a huge amount over the many months it took to prepare it and I hope that some of you learn a lot from reading it. As always, I would love to hear any feedback anyone has on this piece or any other!
I am still working on this series, but I’m not sure yet what the next piece will be. At the top of the list right now is a shorter article about the Feynman path integral formulation of quantum mechanics. Somewhere in the pipe is also a piece about general relativity. I’m always open to suggestions! Send me an e-mail if there’s a topic you’d like to see covered in this style.
My workflow for most of the articles on this site involves producing a TeX document and converting it to HTML after the fact, but I haven’t been releasing PDF copies of the articles even though I have them. That has now changed! At the top of most articles, you will now see a link to a PDF copy. The text is exactly the same, but the PDF might be a better fit for printing or downloading onto an e-reader, so I wanted the option to be available.
I’m also almost done with the next article in the physics for mathematicians series! Expect it before the end of the month.
I’ve posted a new article in the physics for mathematicians series. I’m working on finishing an article for that series about thermodynamics and statistical mechanics, but I’m not done with that one yet. The piece I’ve just finished is on a sort of side question that comes up a lot when learning about thermodynamics: how is it possible for anything like the laws of thermodynamics, which have entropy increasing in only one time direction, to arise from completely time-symmetric microscopic laws of physics? This article explores this question through a toy model which exhibits the same sort of behavior but for which all the relevant computations can be done exactly.
This article is a lot more accessible than the rest of the “physics for mathematicians” series! Anyone with an understanding of the expected value and the variance of a random variable should be totally fine. I felt like this model did a lot for my understanding of the question when I first learned about it, and I hope it can be helpful for you too.
I’ve finally gotten around to posting slides from a three-week lecture series I gave at Google a few months ago called Differential Geometry: Definitions and Pictures. The goal of the talk was to introduce the audience (mostly Google employees working in machine learning) to the way mathematicians think about the subject; there are lots of pictures and intuition and no proofs. The target audience has had a class in multivariable calculus and probably linear algebra.
As always when reading slides without seeing the talk, some parts might not make sense out of context, but I hope this can still be helpful to someone in its current state.