FWIW last I heard, nobody has constructed a pilot-wave theory that agrees with quantum field theory (QFT) in general and the standard model of particle physics in particular. The tricky part is that in QFT there’s observable interference between states that have different numbers of particles in them, e.g. a virtual electron can appear then disappear in one branch but not appear at all in another, and those branches have easily-observable interference in collision cross-sections etc. That messes with the pilot-wave formalism, I think.
Based off the abstracts of these papers:
QFT as pilot-wave theory of particle creation and destruction,
Bohmian Mechanics and Quantum Field Theory,
Relativistically invariant extension of the de Broglie-Bohm theory of quantum mechanics,
Making nonlocal reality compatible with relativity,
Time in relativistic and non relativistic quantum mechanics,
and the Wikipedia page on de Broglie Bohm’s section on QFT, it seems like this claim is wrong. I haven’t read these papers yet, but someone I was talking to said Bohmian QFT is even more unnecessarily complicated than Bohmian QM.
I don’t know if anyone has re-constructed the Standard Model in this framework as of yet.
EDIT: Changed “standard Bohmian QFT” → “Bohmian QM”