[Filligree]

They’re mathematical conveniences; they don’t really exist. There are formalisms such as quantum lattice models in which they aren’t needed.

[jd115]

This isn't really saying anything. What does exist then?

[ben_w]

A dozen (17?) complex-valued (some scalar, some vector) fields, where the square of the absolute value of a field gives the chance of seeing a particle in a given state.

I think. I’m still learning, and from MOOCs and YouTube not a university course.

[Filligree]

The phase space describing those fields, where the measure of each term of the universal wavefunction is equivalent to the amplitude of one point in this space.

Your description suffices for pure states, IIRC. It’s been a while since I did physics.