On the zig-zag pilot-wave approach for fermions

TL;DR

This paper explores a pilot-wave model for fermions based on a zig-zag particle motion with stochastic velocity jumps, extending from single particles to quantum field theory, and analyzing relativistic and non-relativistic limits.

Contribution

It introduces a novel zig-zag pilot-wave approach for fermions, including extensions to many particles and quantum field theory, and examines relativistic and non-relativistic behaviors.

Findings

Single-particle motion is always luminal.

Multi-particle motion can be subluminal.

The approach extends to quantum field theory.

Abstract

We consider a pilot-wave approach for the Dirac theory that was recently proposed by Colin and Wiseman. In this approach, the particles perform a zig-zag motion, due to stochastic jumps of their velocity. We respectively discuss the one-particle theory, the many-particle theory and possible extensions to quantum field theory. We also discuss the non-relativistic limit of the one-particle theory. For a single particle, the motion is always luminal, a feature that persists in the non-relativistic limit. For more than one particle the motion is in general subluminal.