I see. It seems more natural for quantum mechanics than for general relativity, though. In GR, the metric is a living, breathing thing, and I don't see how to s

I see. It seems more natural for quantum mechanics than for general relativity, though. In GR, the metric is a living, breathing thing, and I don't see how to shoehorn that into GA. Similarly, differential geometry gives you a nice, mechanistic way to think about coordinate transformations, including accelerated/rotating coordinates. Similarly, there's Littlejohn's work on applying "normal" differential geometry to plasma physics. I've not read nearly as much about that as I would like to, but it always seemed like fun stuff. I don't think this kind of notation helps with that.