[kurthr]

bra-ket is the (most?) general form of tensor manipulation.

Raising and lowering operators for summation notation are the beginner tools for covariant derivatives of the metric tensor.

Christoffel symbols are where it's at, if you need to write out the Ricci tensor. The more constrained the space the more concise the notation can be.

Note that MechE tensor notation has an even more compact (eigen) form for principal stresses.

[LogicFailsMe]

All of this is true, but I don't believe and I want to be wrong about this that there is something in this notation that starts at an ELI 5 level and gently guides you to physicist level expertise. I all but majored in math (deriving back prop was trivial once it was clear it was the chain rule as one example) but I have never been able to keep bra ket notation straight in my head for the more exotic operations. Einsteinian notation on the other hand is a few minutes of furled brows and then all is clear.

It is what has separated me from being able to code just about anything on a GPU and being known for some of that work and coming up with a better way to run ab initio quantum chemistry on them.

It truly has been my Waterloo for many years. So make me wrong.

[kurthr]

Yeah, bra-ket is arbitrary tensors (inner and outer multiplication) rather than the nice 4D of space-time (with derivatives).

I will say that seeing transformers written this way gives me a bit more intuition for what is going on (being able to identify correct equations), but there's enough complexity in actual transformer implementations, that it still feels like I'm fooling myself.

Conceivably, I think you could use Feynman diagrams to talk about phonon dispersion in (eg asymetric crystaline) solids, but even though they're a "simplification", they're overkill for the problem.

[neutrinobro]

I don't think there is anything in this article that actually demands bra-ket notation (a state in some Hilbert space), that couldn't be more clearly written with standard notation for a Euclidean inner/outer product, but I suppose everyone has their own preferences for notation.