And then there are us engineers. I don't care much either way whether Maxwell's equations are ∇F = J or some other form, as long as it makes the problem easier to solve.
replyIf I were in the GA Marketing Committee I'd publish a paper with suitably hand-picked worked examples where the vector approach is long and tedious, and GA version is short and sweet.
I like this idea but I get the sinking feeling GA proponents don't really solve problems with GA. Like how Haskell advocates don't write programs and modular synth enthusiasts don't write music.
replyApplication of the Method of Moments to solve full wave formulation of Maxwell's equations. To derive the EFIE using maxwell's equations is a massive pain. With geometric algebra, all you need is ∇F = J and the MoM becomes a mechanical process.
replyI guess I'd say my point though is that the gauge structure is the mathematically interesting part of Maxwell's equations. (i.e. the fact that `F` is a closed differential form).
replyWithout it, I think it'd be of significantly less mathematical interest because it'd lose almost all of its geometric properties.
There isn't just ONE interesting facet of this. There isn't just ONE mathematical formalism of a lot of these things. GA is just one of those approaches and you should see it just once, just like you should see the group structure and all of that as well. For most applications, the standard vector calculus approach is fine. But the math underlying all of this is full of richness and no one approach is the skeleton key.
replySame with programming languages. Some people are like RUST RUST RUST and some are like C C C! I'm like, you guys only use one language?