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Wrong. Bohmian mechanics generalizes nicely to interacting relativistic QFT.For example, the concept of interacting particles in relativistic QFT is approximate only, and apart from my own work I don't know any discussion of how this affects interpretation issues. For example, Bohmian mechanics does not generalize to interacting relativistic QFT.

The standard reference to Bohmian QFT is

Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory, Phys. Reports 144(6), 321-375

With the field ontology, that means, the fields ##q = \{\varphi(x)\} \in Q \cong C^\infty(\mathbb{R}^3)## defining the configuration, the interaction terms are simply part of the classical potential ##V(q)##, something one does not have to care at all.

Of course, one should be aware that QFT is simply not a well-defined theory. The only well-defined theories in the whole game are the regularizations. And even most regularizations make no sense as well-defined quantum theories.

All what matters is that there has to be at least one regularization which is also a well-defined quantum theory. For this purpose, I recommend lattice regularizations on a large cube with periodic boundary conditions. Such a lattice theory has already a finite number of degrees of freedom, and the usual scheme works without problems. (Or, more accurate in the context of the question, with exactly the same problems as non-relativistic QM.)

So, the generalization of dBB to the part of QFT which is mathematically well-defined (which is not the limit of the lattice spacing going to zero) is unproblematic.

If one interprets QFT as an effective field theory, so that it does not have to be well-defined for arbitrary small distances, but only for distances larger than some critical distance, there is no point in considering this limit at all, thus, everything is fine.

If one thinks that the relativistic and gauge symmetries are somehow fundamental, then one has some problem with such lattice approximations, given that they have no relativistic symmetry and allow gauge symmetry only for vector gauge fields. (Once the observable massless gauge fields, QCD and EM, are vector gauge fields, the last is no problem too. The massive gauge fields are non-renormalizable, but as effective field theories they would be fine too, as well as gravity.) But the idea that relativistic symmetry is fundamental is not compatible with dBB theory (as well as with any other realist interpretation because of Bell's theorem) anyway. So, with QFT understood as an effective field theory dBB has no problems.