Your first paragraph is reasonable, but quantum physics works in discrete systems. The most extreme case is quantum computation, which often uses finite dimensional Hilbert spaces. But older and more mainstream is lattice gauge theory, which I believe approximates QFT with a discrete quantum system.
Your first paragraph is reasonable, but quantum physics works in discrete systems. The most extreme case is quantum computation, which often uses finite dimensional Hilbert spaces. But older and more mainstream is lattice gauge theory, which I believe approximates QFT with a discrete quantum system.
You can approximate it with a discrete system. It’s just not what quantum physics uses.
Maybe lattice gauge theory isn’t what reality uses, but it’s still quantum physics.