Pilot Wave Theory and Quantum Fields

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Lienert, Matthias
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preprint description
Pilot wave theory (PWT), also called de Broglie-Bohm theory or Bohmian Mechanics, is a deterministic nonlocal `hidden variables' quantum theory without fundamental uncertainty. It is in agreement with all experimental facts about nonrelativistic quantum mechanics (QM) and furthermore explains its mathematical structure. But in general, PWT describes a nonequilibrium state, admitting new physics beyond standard QM. This essay is concerned with the problem how to generalise the PWT approach to quantum field theories (QFTs). First, we briefy state the formulation of nonrelativistic PWT and review its major results. We work out the parts of its structure that it shares with the QFT case. Next, we come to the main part: We show how PW QFTs can be constructed both for field and particle ontologies. In this context, we discuss some of the existing models as well as general issues: most importantly the status of Lorentz invariance in the context of quantum nonlocality. The essay concludes with a more speculative outlook in which the potential of PWT for open QFT questions as well as quantum nonequilibrium physics are considered.