Linking to Wikipedia on an advanced math concept was probably a bit futile, those generally don’t explain much to anyone not already familiar with the thing. The Hestenes article, and this tutorial article are the ones I’ve been reading and can sort of follow, but once they get into talking about how GA is the greatest thing ever for Pauli spin matrices, I have no idea what to make of it.
The tutorial article is much easier to follow, yes. Now, it’s been years since I did anything with Pauli spinors, and one reason for that is that they rather turned me off theory; I could never understand what they were supposed to represent physically. This idea of seeing them as a matrix expression isomorphic to a geometric relation is appealing. Still, I couldn’t get to the point of visualising what the various operations were doing; I understand that you’re keeping track of objects having both scalar and vector components, but I couldn’t quite see what was going on as I can with cross products. That said, it took me a while to learn that trick for cross products, so quite possibly it’s just a question of practice.
Linking to Wikipedia on an advanced math concept was probably a bit futile, those generally don’t explain much to anyone not already familiar with the thing. The Hestenes article, and this tutorial article are the ones I’ve been reading and can sort of follow, but once they get into talking about how GA is the greatest thing ever for Pauli spin matrices, I have no idea what to make of it.
The tutorial article is much easier to follow, yes. Now, it’s been years since I did anything with Pauli spinors, and one reason for that is that they rather turned me off theory; I could never understand what they were supposed to represent physically. This idea of seeing them as a matrix expression isomorphic to a geometric relation is appealing. Still, I couldn’t get to the point of visualising what the various operations were doing; I understand that you’re keeping track of objects having both scalar and vector components, but I couldn’t quite see what was going on as I can with cross products. That said, it took me a while to learn that trick for cross products, so quite possibly it’s just a question of practice.