QFT AS PILOT-WAVE THEORY OF PARTICLE CREATION AND DESTRUCTION

Abstract

States in quantum field theory (QFT) are represented by many-particle wave functions, such that a state describing n particles depends on n space–time 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 four-dimensional Minkowski space–times. 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 one 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 space–time coordinates, then the 4-velocity of the corresponding particle vanishes, describing a trajectory that stops at a particular point in space–time. In a more general situation a dependence on this space–time 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.