[blablabla123]

Not sure, vector calculus isn't very intuitive either if you start with it, with Pauli/gamma matrices it's even worse. Having studied Physics myself, I haven't encountered one lecture where they were able to give a reasonable geometric explanation. (Symplectic Geometry and GA provide it) IMHO if the the same amount of effort was used to force vector calculus into people's heads, it should be doable with these tools as well. Unfortunately there is already a lack of books about the topics

[Koshkin]

> vector calculus isn't very intuitive either

That's, by the way, why we have the calculus of differential forms which, unlike vectors with all their flavors (free; polar; axial/pseudo), have a clear geometric meaning, and with which many statements about fields acquire an especially simple form. There are many excellent guides; for the motivation, see, for example, https://www.jpier.org/PIER/pier148/09.14063009.pdf

[onedognight]

Differential forms are a sub-algebra of the geometric algebra, so you don’t give up any of the beautiful things you mentioned.

[fango]

yes ... V.I.Arnold - important symplectic geometry author tells us: "Hamilton mechanics cannot be understood without differential forms ...". Thanks for your link.