QFT as pilot-wave theory of particle creation and destruction

TL;DR

This paper proposes a pilot-wave interpretation of quantum field theory that provides a deterministic, continuous description of particle creation and destruction through particle trajectories in spacetime.

Contribution

It introduces a pilot-wave framework for QFT that models particle creation and destruction as continuous, deterministic trajectories, extending the de Broglie-Bohm interpretation to quantum fields.

Findings

Wave function as a pilot wave guiding particles in QFT.

Deterministic trajectories describe particle creation and destruction.

Consistent probabilistic predictions of standard QFT are recovered.

Abstract

States in quantum field theory (QFT) are represented by many-particle wave functions, such that a state describing n particles depends on n spacetime positions. Since a general state is a superposition of states with different numbers of particles, the wave function lives in the configuration space identified with a product of an infinite number of 4-dimensional Minkowski spacetimes. The squared absolute value of the wave function is interpreted as the probability density in the configuration space, from which the standard probabilistic predictions of QFT can be recovered. Such a formulation and probabilistic interpretation of QFT allows to interpret the wave function as a pilot wave that describes deterministic particle trajectories, which automatically includes a deterministic and continuous description of particle creation and destruction. In particular, when the conditional wave function associated with a quantum measurement ceases to depend on one of the spacetime coordinates, then the 4-velocity of the corresponding particle vanishes, describing a trajectory that stops at a particular point in spacetime. In a more general situation a dependence on this spacetime coordinate is negligibly small but not strictly zero, in which case the trajectory does not stop but the measuring apparatus still behaves as if this particle has been destroyed.